ALPERTON COMMUNITY SCHOOL
MATHS FACULTY
ACHIEVING GRADE C
EXAM PRACTICE BY TOPIC
WEEK 3
NOTE: questions marked * = you may use a calculator
Each set of questions is followed by solutions so you can check & mark your
own work
CONTENTS
TOPIC
PAGE
NUMBER
GCSE
GRADE
NUMBER – limits / bounds
2
C
ALGEBRA – expanding &
simplifying single & double
brackets
4
C
ALGEBRA – factorising
8
C
ALGEBRA – Solving linear
equations
11
C
STATISTICS – probability
16
C
GEOMETRY – area
20
C
GEOMETRY – Pythagoras
27
C
GEOMETRY – transformations
30
C
Date
Marks
completed
1
Alperton Community School Maths Department: GCSE Grade C Exam Practice
NUMBER – LIMITS & BOUNDS
1.
The weight of a bag of potatoes is 25 kg, correct to the nearest kg.
(a)
Write down the smallest possible weight of the bag of potatoes.
............................... kg
(1)
(b)
Write down the largest possible weight of the bag of potatoes.
............................... kg
(1)
(Total 2 marks)
2.
The length of a line is 63 centimetres, correct to the nearest centimetre.
(a)
Write down the least possible length of the line.
........................................ centimetres
(1)
(b)
Write down the greatest possible length of the line.
........................................ centimetres
(1)
(Total 2 marks)
*3.
Katy drove for 238 miles, correct to the nearest mile.
She used 27.3 litres of petrol, to the nearest tenth of a litre.
Petrol consumption =
Number of miles travelled
Number of litres of petrol used
Work out the upper bound for the petrol consumption for Katy’s journey.
Give your answer correct to 2 decimal places.
...................................... miles per litre
(Total 3 marks)
2
Alperton Community School Maths Department: GCSE Grade C Exam Practice
SOLUTIONS:
1.
(a)
24.5
1
B1 cao
(b)
25.5
1
B1 for 25.5 or 25.49
[2]
2.
(a)
62.5
1
B1 cao
(b)
63.5
1
B1 for 63.5 (accept or 63.49 or 63.49.. any evidence
that the 9 is recurring or 63.499 or better)
[2]
3.
238 has an UB 238.5, a LB of 237.5
27.3 has an UB of 27.35, a LB of 27.25
Upper:
238.5
= 8.75229
27.25
8.75
3
B1 for one of 238.5, 237.5, 27.35, 27.25, 238.49 ,
27.349 seen
M1 for ‘UB no of miles’ ÷ ‘LB no of litres’
Where 238< ‘UB no of miles’ ≤ 238.5 and 27.25 ≤
‘LB no of litres’ < 27.3
A1 8.75 or 8.752 or 8.7522 or 8.7523 or better
SC 238.4 27.25 which leads to 8.748…B1 M1 A0
[3]
3
Alperton Community School Maths Department: GCSE Grade C Exam Practice
ALGEBRA – EXPANDING &
SIMPLIFYING
1.
(a)
Simplify
(i)
3g + 5g.................................
(ii)
2r × 5p.................................(2)
(b)
Expand
5(2y – 3).................................(1)
(c)
Expand and simplify
2(3x + 4) – 3(4x – 5).................................
(2) (Total 5 marks
2.
(a)
Expand and simplify 3(2x – 1) – 2(2x – 3)
…………………………(2)
3.
(a)
(b)
Factorise p2 + 6p
…………………….(2)
Expand and simplify (x + 7)(x – 4)
…………………….(2) (Total 4 marks)
4.
(a)
Expand and simplify (x + 7)(x – 4)
…………………….(2)
(b)
Expand y(y3 + 2y)
…………………….(2)
5.
(c)
Factorise p 2 + 6p
(a)
Simplify 4p + 5q + p – 3q.....................................(2)
(b)
Expand y(y – 5).....................................(1)
(c)
Expand and simplify 2(3m + 4) + 3(m – 5)
…………………….(2)
.....................................(2) (Total 5 marks
4
Alperton Community School Maths Department: GCSE Grade C Exam Practice
6.
(a)
Simplify 4a + 3c – 2a + c.....................................(1)
(b)
S=
1 2
at
2
Find the value of S when t = 3 and a =
1
4
S = ......................................(2)
x2 – 5x.....................................(2)
(c)
Factorise
(d)
Expand and simplify
(x + 3)(x + 4)
...................................................(2)
7.
(a)
Expand and simplify
3(x + 4) + 5(2x + 1)
.....................................(2)
(b)
Simplify t4 × t6.....................................(1)
(c)
Simplify p8 ÷ p5.....................................(1)
(d)
Simplify (x4)3.....................................(1)
(Total 5 marks)
8.
(a)
Simplify
a × a × a............................(1)
(b)
Expand
5(3x – 2)........................................(1
(c)
Expand
3y(y + 4)........................................(2)
(d)
Expand and simplify
2(x – 4) + 3(x + 2)
............................(2)
(e)
Expand and simplify
(x + 4)(x – 3)
........................................(2) (Total 8 marks
9.
Expand and simplify 2(3x + 4) – 3(4x – 5)
.................................(Total 2 marks)
5
Alperton Community School Maths Department: GCSE Grade C Exam Practice
10.
Expand
(x + 5)(x + 8)
…………………………(Total 2 marks)
11.
Expand and simplify
(x + 7)(x + 5)
............................... (Total 2 marks)
12.
Expand and simplify (x – 9)(x + 4)
................................ (Total 2 marks)
13.
Expand and simplify
(x + 1)(x – 7)
........................................ (Total 2 marks)
14.
Expand
5(2w – 3)
(Total 1 mark
15.
Expand and simplify (x − 2)(x + 1)
.....................................(Total 2 marks)
16.
(a)
Expand c(d + 4)
.....................................(1)
(b)
Expand and simplify 3(x + 5) + 2(x – 1)
.....................................(2) (Total 3 marks)
17.
(a)
Expand and simplify
4(2x + 5) + 2(3x – 2)
..................................(2)
(b)
Expand and simplify
(x + 5) (x + 8)
...................................(2) (Total 4 marks)
6
Alperton Community School Maths Department: GCSE Grade C Exam Practice
SOLUTIONS:
1.
(a)
(i)
(b)
10y − 15
(a)
2x + 3
(b)
y (y + 1)
3.
(a)
p(p + 6)
4.
(a)
x2 +3x – 28
2.
8g
(ii)10rp
(c)− 6x + 23
(6x – 3 – 4x + 6 = 2x + 3)
(b) x2 + 3x – 28 (x2 – 4x + 7x – 28)
(x2 – 4x + 7x – 28)
y4 + 2y2
(b)
(c)
p(p + 6)
(d)
3x(2x – 3y)
5.
(a)
5p + 2q
6.
(a)
2a + 4c
(b)
½ × ¼ × (3)2 = ½ × ¼ × 9 = 1.125
1.125
(c)
x(x – 5)
(d)
x2 + 3x + 4x + 12 = x2 + 7x + 12
(e)
(y + 3)(y + 5)
7.
(a)
13x + 17 (b) t10
8.
(a)
a3
(b)
5 × 3x – 5 × 2 = 15x – 10
(c)
3y × y + 3y × 4 = 3y2 + 12y
(d)
2x – 8 + 3x + 6 = 5x – 2
(e)
x2 + 4x – 3x – 12 =
9.
(6x + 8 − 12x + 15)
(b) y2 – 5y
(c) p3
(c)
6m + 8 + 3m – 15 = 9m – 7
(d) x12
x2 + x – 12
− 6x + 23 (6x + 8 − 12x + 15)
2x − 24
x2 − 6x + 4x − 24
10.
x2 + 8x + 5x + 40 = x2 + 13x + 40
11.
x2 + 12x + 35 (x2 + 5x + 7x + 35)
12.
x2 – 5x –36
13.
x2 – 7x + x – 7 = x2 – 6x – 7
14.
10w – 15
15.
x2 + x – 2x – 2 = x2 – x – 2
16.
(a)
cd + 4c
(b)
3x + 15 + 2x – 2 = 5x + 13
(a)
8X+20+6X-4 = 14X + 16
17.
(x2 + 4x – 9x– 36)
b) x2 +8 x+5x+40 = x2 +13x+40
7
Alperton Community School Maths Department: GCSE Grade C Exam Practice
ALGEBRA – FACTORISING
1.Factorise t2 – 5t………………………
(2)
2.
(a)
Factorise
3t – 12………………………
(1)
(b)
Expand and simplify 3(2x – 1) – 2(2x – 3)
…………………………(2 (Total 3 marks)
3.
(a)
Expand and simplify
3(2x – 1) – 2(2x – 3)
…………………………(2)
(b)
Factorise y2 + y…………………………(1) (Total 3 marks)
4.
Factorise x2 – 3x......................... (Total 2 marks)
5.
(a)
Expand
t(t – 2)..........................(1)
(b)
Factorise
3y – 12..........................(1) (Total 2 marks)
(c).
Factorise fully
2p2 – 4pq
..........................(2) (Total 5 marks)
6.
Factorise p2 + 6p…………………….(2)
(a)
(b)
Expand and simplify (x + 7)(x – 4)…………………….(2)
(Total 4 marks)
7.
Factorise
8.
(a)
Simplify fully 4a + 5b – 2a + b.....................................(2)
Factorise x2 – 6x.....................................(2)
(b)
9.
x2 – 3x.................................(Total 2 marks)
(c)
Expand x(3 – 2x2).....................................(2)
(d)
Factorise completely 12xy + 4x2.....................................(2) (Total 8 marks)
(a)
Factorise x2 – 5x.....................................(2)
(b)
Factorise completely 3a2 – 6a.....................................(2)
8
Alperton Community School Maths Department: GCSE Grade C Exam Practice
10.
11.
(c)
Factorise x2 – 5x..........................................(1)
(b)
Factorise x2 – 36.............................................(1)
(e)
Factorise
y2 + 8y + 15...................................................(2)
(a)
Factorise
5m + 10................................(1)
(b)
Factorise
y2 – 3y................................(1) (Total 2 marks)
(a)
Factorise fully
4x2 – 6xy.....................................(2)
(b)
Factorise
x2 + 5x – 6.....................................(2) (Total 4 marks)
12.
Factorise
13.
(a)
14.
Factorise
15.
Simplify fully
(a)
(b)
16.
Factorise
3m + 15……………………………(1 mark)
9x2 – 6x + 1……………………………(2)
x2 + 7x + 6..........................(Total 2 marks)
(3xy2)4…………………….(2)
x 2 − 3x
…………………….(3) (Total 5 marks)
x 2 − 8 x + 15
(a)
Factorise
x2 + 6x + 8………………………(2)
(b)
Solve
x2 + 6x + 8 = 0
x =………………………
or x =………………………(1)
(Total 3 marks)
9
Alperton Community School Maths Department: GCSE Grade C Exam Practice
SOLUTIONS:
1. t(t-5)
2a. 3(t-4)
(b) 6x-3-4x+6 = 2x+3
3. (a)
6x-3-4x+6 = 2x+3
4.
x(x-3)
5.
(a)
6.
(a)
7.
x(x-3)
8.
(a)
2a+6b
9.
(a)
x(x – 5)
t2 -2t
(b)
p(p+6)
3(y-4)
(b)
(b)
(b)
y(y+1)
c) . 2p(p-2q)
x2 -4x+7x-28 = x2 +3x-28
x(x-6)
(b) 3a(a-2)
(c)
3x-6x2
(c) x(x-5)
(d)
4x(3y+x)
(b) (x-6)(x+6)
(e) (y+3)(y+5)
10.
11.
(a)
5(m + 2)
(b)
y(y – 3)
(a)
2x(2x-3y)
(b)
(x-1)(x+6)
12. 3(m + 5)
13.
(x+6)(x+1)
14.
Simplify fully
(a)
(b)
81x4y8
x 2 − 3x
…………………….(3) (Total 5 marks)
x 2 − 8 x + 15
15.
(a)
(x+4)(x+2)
(b)
x=-4 x=-2
10
Alperton Community School Maths Department: GCSE Grade C Exam Practice
ALGEBRA – SOLVING LINEAR
EQUATIONS
1.
(a)
Solve
7p + 2 = 5p + 8
p = ............................(2)
(b)
Solve
7r + 2 = 5(r – 4)
r = ........................... (2) (Total 4 marks)
2.
(a)
Solve 7x + 18 = 74
x = ………………………(2)
(b)
Solve 4(2y – 5) = 32
y = ………………………(2)
(c)
Solve 5p + 7 = 3(4 – p)
p = ………………………(3) (Total 7 marks)
3.
Nassim thinks of a number. When he multiplies his number by 5 and subtracts 16 from
the result, he gets the same answer as when he adds 10 to his number and multiplies that result
by 3. Find the number Nassim is thinking of.
……………………………(Total 4 marks)
*4.
Martin cleaned his swimming pool. He hired a cleaning machine to do this job.
The cost of hiring the cleaning machine was
£35.50 for the first day,
then £18.25 for each extra day. Martin’s total cost of hiring the
machine was £163.25
For how many days did Martin hire the machine?
.................. days (Total 3 marks)
11
Alperton Community School Maths Department: GCSE Grade C Exam Practice
5.
(a)
Solve
20y – 16 = 18y – 9
y = ....................(3)
(b)
40 – x
=4+x
3
Solve
x = ....................(3) (Total 6 marks)
6.
Jo buys 8 cups and 8 mugs. A cup costs £x.
(a)
A mug costs £(x + 2)
Write down an expression, in terms of x, for the total cost, in pounds, of 8 cups
and 8 mugs.
£..............................(2)
The total cost of 8 cups and 8 mugs is £72
(b)
(i)
Express this information as an equation in terms of x.
....................................(1)
(ii)
Solve your equation to find the cost of a cup and the cost of a mug.
Cost of a cup £ ..............................Cost of a mug £ ..............................(4) (Total 7 marks)
7.
(a)
Solve
4(2x + 1) = 2(3 – x)
x = ..........................(3)
12
Alperton Community School Maths Department: GCSE Grade C Exam Practice
8.
(a)
Solve 5 – 3x = 2(x + 1)
x = ………………….(3)
(b)
–3 ≤ y < 3 y is an integer. Write down all the possible values of y.
…………………….(2) (Total 5 marks)
*9.
Cinema Ticket Prices
Adults
£4
Child
£3
An adult ticket costs £4. A child ticket costs £3.
(a)
Write down a formula for the total cost, £T, for n adult tickets and c child tickets.
.................................(3)
Hina spends £47 on cinema tickets. She buys 8 adult tickets.
(b)
Work out how many child tickets she buys.
.................................(3) (Total 6 marks)
10.
Solve
5(2y + 3) = 20
y = .................................(Total 3 marks)
11.
Solve
4y + 1 = 2y + 8
y =………………………(Total 2 marks)
12.
Solve
4x + 3 = 19
x =………………………(Total 2 marks
13.
Solve 6x – 5 = 2x + 9
x = ..............................
(Total 3 marks)
13
Alperton Community School Maths Department: GCSE Grade C Exam Practice
14.
A
2x
B
2x
C
10
In the diagram, all measurements are in centimetres.
ABC is an isosceles triangle. AB = 2x AC = 2x BC = 10
(a)
Find an expression, in terms of x, for the perimeter of the triangle. Simplify your
expression.
………………………(2)
The perimeter of the triangle is 34 cm. (b)
Find the value of x.
x =………………………(2) (Total 4 marks)
15.
Diagram NOT accurately drawn
In the diagram, all measurements are in centimetres. The lengths of the sides of the
quadrilateral are
2r + 5 2r
(a)
4r – 3 r
Find an expression, in terms of r, for the perimeter of the quadrilateral.
Give your expression in its simplest form..........................................(2)
The perimeter of the quadrilateral is 65 cm. (b) Work out the value of r.
r = .....................................(2) (Total 4 marks)
14
Alperton Community School Maths Department: GCSE Grade C Exam Practice
SOLUTIONS:
1.
(a)
p=3 (b) r=11
2.
(a)
8
(b)
6.5 (8y – 20 = 32 or 2y – 5 = 8
(c)
5
2
7x = 56
8p + 7 = 12 or 5p = 5 – 3p
8y = 52 2y = 13)
8p = 5 8p = 5
8
3.
23
4
5x – 16 = 3(x + 10)
5x –16 = 3x + 30
5x – 3x = 30 + 16
2x = 46
4.
8
5.
(a)
163.25 – 35.50 = 127.75
127.75 ÷ 18.25 = 7
3½ oe
3
20y – 18y = 16 – 9 2y = 7
(b)
7
3
40 – x = 3(4 + x)
40 – x = 12 + 3x
40 – 12 = x + 3x
4x = 28
6.
(a)
8x + 8(x + 2) (b) (i) 8x +8(x + 2) = 72
(ii)
5
£3.50 £5.50
8x + 8x + 16 = 72 16x = 72 – 16
7.
(a)
0.2
3
8x+ 4 = 6 – 2x
8.
(b)
2p(p – 2q)
(a)
3
5
5 – 3x = 2x + 2
9.
8x+2x= 6 – 4
5 – 2 = 2x + 3x
(b)
– 3, – 2, – 1, 0, 1, 2
(a)
T = 4n + 3c
(b)
47 = 4 × 8 + 3c
3c = 47 – 32 3c = 15 5
10.
10y + 15 = 20 10y = 20 – 15 y = 5/10
11.
(a)
2x + 2x + 10
(b)
4x + 10 = 34
= 0.5
4x + 10
3
3
2
6
2
12.
4x = 16
4
2
13.
4y – 2y = 8 – 1 3.5
14.
6x – 2x = 9 + 5 4x = 14
15.
(a)
r + 2r + 5 + 2r + 4r – 3 = 9r + 2
2
(b)
9r + 2 = 65 = 7
2
2
=3
1
2
STATISTICS – PROBABILITY
15
Alperton Community School Maths Department: GCSE Grade C Exam Practice
*1.
Four teams, City, Rovers, Town and United play a competition to win a cup. Only one
team can win the cup.
The table below shows the probabilities of City or Rovers or Town winning the cup.
City
Rovers
Town
United
0.38
0.27
0.15
x
Work out the value of x..........................(Total 2 marks)
2.
The table shows information about the number of fillings the students in a class had last
year.
Number of
fillings
Number of
students
0
10
1
5
2
4
3
2
More than 3
1
The headteacher is to choose a student at random from the class.
Find the probability that she will choose a student who had
(a)
exactly 1 filling,…………………(1)
(b)
2 or more fillings,…………………(1)
(c)
either 1 filling or 2 fillings.…………………(1)
(Total 3 marks)
3.
The probability that a biased dice will land on a four is 0.2 Pam is going to roll the dice
200 times. Work out an estimate for the number of times the dice will land on a four.
.........................(Total 2 marks)
*4.
Mr Brown chooses one book from the library each week.He chooses a crime novel or a
horror story or a non-fiction book. The probability that he chooses a horror story is 0.4
The probability that he chooses a non-fiction book is 0.15 Work out the probability that
Mr Brown chooses a crime novel.…………………….
(Total 2 marks)
5.
Here is a 4-sided spinner.
16
Alperton Community School Maths Department: GCSE Grade C Exam Practice
The sides of the spinner are labelled 1, 2, 3 and 4. The spinner is biased.
The probability that the spinner will land on each of the numbers 2 and 3 is given in the
table.
The probability that the spinner will land on 1 is equal to the probability that it will land
on 4.
(a)
Number
1
2
3
4
Probability
x
0.3
0.2
x
Work out the value of x.x = ………………….(2)
Sarah is going to spin the spinner 200 times.
(b)
Work out an estimate for the number of times it will land on 2
…………………….(2) (Total 4 marks)
*6.
A school snack bar offers a choice of four snacks. The four snacks are burgers, pizza,
pasta and salad. Students can choose one of these four snacks.
The table shows the probability that a student will choose burger or pizza or salad.
Snack
Probability
burger
pizza
0.35
0.15
pasta
salad
0.2
One student is chosen at random from the students who use the snack bar.
(a)
Work out the probability that the student
(i)
did not choose salad,.................................
(ii)
chose pasta..................................(3)
300 students used the snack bar on Tuesday.
(b)
Work out an estimate for the number of students who chose pizza.
.................................
(2)
(Total 5 marks)
17
Alperton Community School Maths Department: GCSE Grade C Exam Practice
7.
70 students each chose one P.E. activity. They chose one of basketball or swimming or
football. The two-way table shows some information about their choices.
Basketball
Swimming
Total
10
Female
37
17
Male
19
Total
(a)
Football
22
70
Complete the two-way table.(3)
One of these students is picked at random.
(b)
Write down the probability that this student chose basketball.
.......................................(2) (Total 5 marks)
8.
Joe rolls a 6-sided dice and spins a 4-sided spinner. The dice is labelled 1, 2, 3, 4, 5, 6
4
1
4
3
The spinner is labelled 1, 2, 3, 4
2
Joe adds the score on the dice and the score on the spinner to get the total score. He
records the possible total scores in a table
+
1
2
3
4
5
6
1
2
2
3
3
4
4
5
3
4
5
6
7
(a)
Complete the table of possible total scores.(2)
(b)
Write down all the ways in which Joe can get a total score of 5 One of them has
been done for you. (1, 4), .....................................(2)
(c)
Write down all the ways Joe can get a total score of 8 or more........................(2)
(Total 6 marks)
9.
There are 3 red pens, 4 blue pens and 5 black pens in a box. Sameena takes a pen, at
random, from the box.
Write down the probability that she takes a black pen.
........................(Total 2 marks
18
Alperton Community School Maths Department: GCSE Grade C Exam Practice
SOLUTIONS:
1.
0.20
0.38 + 0.27 + 0.15
2.
(a)
5
(b)
22
3.
40
200 × 0.2
4.
0.45
0.4 + 0.15
5.
(a)
7
(c)
22
9
22
1 – “0.55”
0.25
x + 0.3 + 0.2 + x =1
(b)
60
0.3 × 200
6.
7.
(b)
8.
9.
(a)
(i)
1 – 0.2 = 0.8
(ii)
1 – (0.35 + 0.15 + 0.2) = 0.3
(b)
0.15 × 300 = 45
(a)
10
9
19
12
17
29
15
7
22
37
33
70
19
70
(a)
45678
56789
6 7 8 9 10
(b)
(1, 4); (2, 3); (3, 2); (4, 1)
(c)
(2, 6); (3, 5); (3, 6); (4, 4); (4, 5); (4, 6)
5
12
19
Alperton Community School Maths Department: GCSE Grade C Exam Practice
GEOMETRY – AREA
*1.
Diagram NOT
accurately drawn
4.5 m
2.8 m
3.2 m
The diagram represents a large tank in the shape of a cuboid. The tank has a base.
It does not have a top. The width of the tank is 2.8 metres. The length of the tank is 3.2 metres.
The height of the tank is 4.5 metres. The outside of the tank is going to be painted. 1 litre of
paint will cover 2.5 m2 of the tank. The cost of paint is £2.99 per litre. Calculate the cost of the
paint needed to paint the outside of the tank.
£ ..................................(Total 5 marks)
*2.
Diagram NOT
accurately drawn
15 cm
The diagram shows a semi-circle. The diameter of the semi-circle is 15 cm.
Calculate the area of the semi-circle. Give your answer correct to 3 significant
figures.............................(Total 3 marks)
*3.
20 cm
Diagram NOT
accurately drawn
9 cm
4 cm
8 cm
The diagram shows a shape. Work out the area of the shape.
…………………………… cm2 (Total 4 marks)
*4.
Mary’s floor is a rectangle 8 m long and 5 m wide. She wants to cover the floor
completely with carpet tiles. Each carpet tile is square with sides of length 50 cm.
Each carpet tile costs £4.19 Work out the cost of covering Mary’s floor completely with
carpet tiles.
£ ..............................(Total 3 marks)
20
Alperton Community School Maths Department: GCSE Grade C Exam Practice
*5.
The diameter of a circle is 12 centimetres.
(a)
Work out the circumference of the circle.
Give your answer, in centimetres, correct to 1 decimal place.
Diagram NOT
drawn accurately
12 cm
.............................. cm (2)
Diagram NOT
accurately drawn
The length of each diagonal of a square is 20 cm.
(b)
Work out the area of the square.
.............................. cm2 (2) (Total 4 marks)
*6.
The diagram shows a wall with a door in it.
4m
1m
Diagram NOT
accurately drawn
3m
2m
Work out the shaded area.…………………m2(3)
(a)
Meg can cover the shaded area with 680 tiles. She buys extra tiles in case she breaks
some. To work out the total number of tiles to buy, Meg increases 680 by 10%.
(b)
(i)
Increase 680 by 10%.……………………..
The tiles Meg is going to use are sold in boxes of 50.
(ii)
Work out the number of boxes of tiles Meg should buy.……………………..(5)
(Total 8 marks)
21
Alperton Community School Maths Department: GCSE Grade C Exam Practice
7.
The width of a rectangle is x centimetres. The length of the rectangle is (x + 4)
centimetres.
(a)
Find an expression, in terms of x, for the perimeter of the rectangle. Give your
expression in its simplest form.…………………….(2)
The perimeter of the rectangle is 54 centimetres.
(b)
8.
Work out the length of the rectangle.…………………cm (3) (Total 5 marks)
The diagram shows a 6-sided shape made from a rectangle and a right-angled triangle.
2 cm
Diagram NOT
accurately drawn
7 cm
12 cm
6 cm
Work out the total area of the 6-sided shape.
...........................cm2 (Total 3 marks)
9.
The diagram shows a trapezium of height 3 m.
2m
Diagram NOT
accurately drawn
3m
6m
Find the area of this trapezium State the units with our answer.................................
(Total 3 marks)
22
Alperton Community School Maths Department: GCSE Grade C Exam Practice
*10.
Diagram NOT accurately drawn
The diagram shows a rectangle inside a triangle. The triangle has a base of 12 cm and a
height of 10 cm. The rectangle is 5 cm by 3 cm. Work out the area of the region shown
shaded in the diagram.
.................................. cm2 (Total 3 marks)
*11.
Diagram NOT
accurately drawn
Work out the total surface area of the L-shaped prism. State the units with your answer.
.....................................(Total 4 marks)
23
Alperton Community School Maths Department: GCSE Grade C Exam Practice
*12.
5 cm
12 cm
Diagram NOT
accurately drawn
(a)
Work out the area of the triangle.………………. cm2 (2)
A
5 cm
P
12 cm
B
5 cm
Q
12 cm
12 cm
S
5 cm
D
12 cm
R
5 cm
C
Diagram NOT
accurately drawn
4 copies of the triangle and the quadrilateral PQRS are used to make the square ABCD.
(b)
Work out the area of the quadrilateral PQRS.………………. cm2 (3)
(Total 5 marks)
*13.
3 cm
5 cm
7 cm
4 cm
Diagram NOT accurately drawn
Work out the total surface area of the triangular prism............................ cm2 (Total 3
marks)
24
Alperton Community School Maths Department: GCSE Grade C Exam Practice
14.
Diagram NOT accurately drawn
7 cm
A
B
8 cm
.
C
13 cm
D
ABCD is a trapezium. Angle A = 90°. Angle D = 90°. AB = 7 cm. AD = 8 cm. DC = 13
cm.
Work out the area of the trapezium.
..................................... cm2 (Total 2 marks)
15.
4 cm
8 cm
4 cm
Diagram NOT accurately drawn
The diagram shows two small circles inside a large circle. The large circle has a radius of
8 cm. Each of the two small circles has a diameter of 4 cm.
(a)
Write down the radius of each of the small circles.
............................. cm
(1)
(b)
Work out the area of the region shown shaded in the diagram.
Give your answer correct to one decimal place.
...................................... cm2 (Total 5 marks)
25
Alperton Community School Maths Department: GCSE Grade C Exam Practice
SOLUTIONS:
1.
£75.30
3.2 × 2.8 = 8.96
62.96
× 2.99
2.5
2.
88.4cm2
3.
102
2 × 4.5 × 2.8 = 25.2
2 × 4.5 × 28.8 = 28.8
2
 15 
 = 176.715
2
π ×
Splits up shape e.g. into rectangle and triangle
9 × 8 or 72
1
×"12"×"5" or 30
2
4.
(a)
(i)
450
5.
(a)
37.7cm
(b)
200cm2
30 × 15
π × 12
0.5 × 10 × 10 = 50
6.
(a)
50 × 4 = 200
10
4×3–2×1
(b)
(i)
12 – 2
748
10
× 680 or 680 ÷ 10
100
(ii)
7.
(a)
4x + 8
(b)
15.5
15
680 + 68
“748” ÷ 50 or 14.96
x+4+x+x+4+x
4x + 8 = 54
4 x = 46
8.
6 × 5 – 2 = 15
9.
Area = 0.5 × (2 + 6) × 3
10.
(a)
3.14 × 50 × 50
(b)
3.14 × 40
11.
A
50
(ii (b)
x = 11.5
Length = “11.5” + 4
15 + 24 = 39
= 0.5 × 8 ×3
= 12 m2
7854
126
2 [(3 × 1) + (4 × 1)] +
(3 × 6) + (1 × 6) + (2 × 6) + (4 × 6) + (1 × 6) + (5 × 6) = 110 cm2
12.
(a)
(b)
1
2
× 12 × 5 = 30
Area ABCD = 172 = 289
Area PQRS = 289 – 4 × “30”
Or (5 + 12)2 = 289
289 – 4 × “30” = 169
13.
1
(3 × 4) × 2 + (3 × 7) + (4 × 7) + (5 × 7) = 12 + 21 + 28 + 35
2
14.
8(7 + 13)
2
15.
(a)
2
96 cm2
80
b) π × 82 – 2 × π × 22
175.9
26
Alperton Community School Maths Department: GCSE Grade C Exam Practice
GEOMETRY – PYTHAGORAS
*1.
3.2 cm
X
Y
Diagram NOT
accurately drawn
1.7 cm
Z
XYZ is a right-angled triangle. XY = 3.2 cm. XZ = 1.7 cm. Calculate the length of YZ.
Give your answer correct to 3 significant figures.
…………………………. Cm (Total 3 marks
*2.
B
A
10 cm
D
Diagram NOT
accurately drawn
17 cm
C
ABCD is a rectangle. AC = 17 cm.\AD = 10 cm.
Give your answer correct to one decimal place.
Calculate the length of the side CD.
................................... cm\(Total 3 marks)
*3.
Diagram NOT accurately drawn
The diagram shows three cities. Norwich is 168 km due East of Leicester. York is 157
km due North of Leicester.
Calculate the distance between Norwich and York.
Give your answer correct to the nearest kilometre.
................................ km (Total 3 marks)
27
Alperton Community School Maths Department: GCSE Grade C Exam Practice
*4.
Diagram NOT
accurately drawn
A rectangular television screen has a width of 45 cm and a height of 34 cm.
Work out the length of the diagonal of the screen.Give your answer correct to the nearest
centimetre.................................. cm (Total 4 marks)
*5.
B
9 cm
A
6 cm
C
Diagram NOT accurately drawn
ABC is a right-angled triangle. AC = 6 cm. BC = 9 cm. Work out the length of AB.
Give your answer correct to 3 significant figures.............................. cm (Total 3 marks)
*6.
L
3.7 m
M
6.3 m
N
Diagram NOT accurately drawn
Angle MLN = 90°.LM = 3.7 m.MN = 6.3 m. Work out the length of LN. Give your
answer correct to 3 significant figures.
LN = ……….…………….. m (Total 3 marks)
28
Alperton Community School Maths Department: GCSE Grade C Exam Practice
SOLUTIONS:
1.72 + 3.22 = 2.89 + 10.24 = 13.13
1.
3.6
2.
13.7cm
3.
1682 + 1572 = 28 224 + 24 649
= 52 873
13.13
172 – 102 = 189
28224 + 24649
229.9 – 230
4.
452 + 342 = 2025 + 1156 = 3181 √3181 = 56.4 = 56
5.
92 – 62 81 – 36 = 45
6.
5.10
45
6.705 – 6.71
√(6.32 − 3.72)
29
Alperton Community School Maths Department: GCSE Grade C Exam Practice
GEOMETRY – TRANSFORMATIONS
1.
y
4
3
B
2
A
1
C
–5
–4
–3
–2
–1
O
x
1
2
3
4
5
–1
–2
–3
–4
Shape A is rotated 90° anticlockwise, centre (0, 1), to shape B Shape B is rotated 90°
anticlockwise, centre (0, 1), to shape C Shape C is rotated 90° anticlockwise, centre (0,
1), to shape D
(a)
Mark the position of Shape D
(2)
(b)
Describe the single transformation that takes shape C to shape A.
..............................................................................................(2) (Total 4 marks)
2.
Triangle A and triangle B have been drawn on the grid.
(a)
Reflect triangle A in the line x = 3. Label this image C. (2)
(b)
Describe fully the single transformation which will map triangle A onto triangle B.
30
Alperton Community School Maths Department: GCSE Grade C Exam Practice
3.
Triangle A and triangle B have been drawn on the grid.
Describe fully the single transformation which will map triangle A onto triangle B.
…………...……………………………………………………………(Total 2 marks
4.
(a)
Describe fully the single transformation that maps triangle A onto triangle B.
................................................................................................................................(2)
(b)
On the grid, rotate triangle A 90º anticlockwise about the point (–1, 1) Label your
new triangle C. (2) (Total 4 marks)
5.
31
Alperton Community School Maths Department: GCSE Grade C Exam Practice
y
6
5
4
3
2
T
1
–6
–5
–4
–3
–2
–1 O
1
2
3
4
5
6
x
–1
–2
–3
–4
–5
–6
Triangle T has been drawn on the grid.
(a)
Reflect triangle T in the y-axis. Label the new triangle A. (1)
(b)
Rotate triangle T by a half turn, centre O. Label the new triangle B. (2)
y
12
11
10
9
8
7
6
C
5
4
3
2
T
1
O
(c)
1
2
3
4
5
6
7
8
9
10
11
12 x
Describe fully the single transformation which maps triangle T onto triangle C.
.....................................................................................................................................
.
............................................................................................(3 (Total 6 marks)
6.
32
Alperton Community School Maths Department: GCSE Grade C Exam Practice
y
5
4
3
A
2
1
–5
–4
–3
–2
–1 O
1
2
3
4
5
x
–1
–2
–3
–4
–5
(a)
On the grid, rotate triangle A 180° about O. Label your new triangle B. (2
(b)
On the grid, enlarge triangle A by scale factor
triangle C.
1
, centre O. Label your new
2
(3) (Total 5 marks)
7.
A pattern is to be drawn.
It will have rotational symmetry of order 4.
The pattern has been started.
By shading six more squares, complete the pattern.
33
Alperton Community School Maths Department: GCSE Grade C Exam Practice
8
y
7
6
5
4
P
3
2
1
–6
–5
–4
–3
–2
–1
O
1
2
3
4
6 x
5
–1
–2
–3
–4
–5
–6
(a)
On the grid, rotate the shaded shape P one quarter turn anticlockwise about O.
Label the new shape Q. (3)
(b)
On the grid, translate the shaded shape P by 2 units to the right and 3 units up.
Label the new shape R. (1) (Total 4 marks)
9.
y
6
5
4
3
2
1
–6
–5
–4
–3
–2
–1 O
1
2
3
4
5
6 x
–1
P
–2
–3
–4
–5
–6
(a)
Rotate triangle P 180° about the point (–1, 1).
(b)
6
Translate triangle P by the vector   .
 −1
Label the new triangle B.
Label the new triangle A. (2)
(1)
34
Alperton Community School Maths Department: GCSE Grade C Exam Practice
y
y=x
5
4
3
2
Q
1
O
(c)
1
2
3
5 x
4
Reflect triangle Q in the line y = x. Label the new triangle C. (2) (Total 5 marks
10.
y
7
6
5
4
3
2
1
–4
–3
–2
–1
O
1
2
3
4
5
6
7
8
x
–1
–2
–3
–4
Enlarge the shaded triangle by a scale factor 2, centre 0. (Total 3 marks)
35
Alperton Community School Maths Department: GCSE Grade C Exam Practice
11.
y
6
5
Q
4
3
P
2
1
–3
–2
–1
O
1
2
3
5 x
4
–1
–2
(i)
Describe fully the single transformation that maps shape P onto shape Q.
(ii)
Reflect shape P in the line x = 1
(Total 5 marks)
12.
y
8
7
6
5
4
3
2
1
O
1
2
3
4
5
6
7
8
9
10
x
On the grid, enlarge the shaded shape by scale factor of 2, centre (1,1).
(Total 3 marks)
36
Alperton Community School Maths Department: GCSE Grade C Exam Practice
13.
y
B
A
x
O
Describe fully the single transformation which takes shape A onto shape B.
………………………………………………………………………(Total 3 marks)
14.
y
3
2
1
–4
–3
–2
–1
O
1
2
3
4
5
x
–1
–2
–3
×
–4
P
–5
Enlarge the shaded triangle by a scale factor 1
1
, centre P.
2
(Total 3 marks)
37
Alperton Community School Maths Department: GCSE Grade C Exam Practice
15.
y
5
4
3
2
1
–5
–4
–3
–2
–1 O
1
2
3
4
x
5
–1
–2
A
–3
–4
–5
Enlarge triangle A by scale factor –
1
, centre (–1, –2). Label your triangle B (Total 3
2
16
y
7
6
5
4
3
2
1
–6
–5
–4
–3
–2
–1 O
1
2
3
4
5
6
x
–1
–2
 4 
Translate the triangle by the vector  
 − 3
(Total 1 mark)
38
Alperton Community School Maths Department: GCSE Grade C Exam Practice
17.
y
8
6
4
2
–8
–6
–4
–2
O
2
4
6
8 x
–2
–4
–6
–8
(a)
Rotate the shaded shape 90° clockwise about the point O. (2)
y
4
3
P
2
Q
1
–3
–4
(b)
–1
–2
O
1
2
3
4
x
Describe fully the single transformation that will map shape P onto shape Q.
....................................................................................................(2) (Total 4 marks)
18.
y
30
28
26
24
22
20
P
18
16
14
12
10
8
6
4
2
O
2
4
6
8
10
12
14
16
18
20
22
24
x
 8
(a) On the grid, translate triangle P by the vector  
 − 3
39
Alperton Community School Maths Department: GCSE Grade C Exam Practice
SOLUTIONS:
1.
2.
(a)
Triangle with vertices at (0, 0) (0, −2) and (3, 0)
(b)
Rotation, 180°, centre (0, 1) Enlargement sf –1 centre (0, 1)
(a)
correct reflection (b) reflection in y = x Reflect the triangle in the line y = 1
3.
2
reflection in y = x
4.
(a)
5.
(a)
reflection line y = x
(b) Triangle with vertices at (–1, 3), (–3, 3) and (–3, 4)
Reflection in y-axis
(b)
Rotation by half turn about (0, 0)
9.
11.
(c)
Enlargement Scale factor 3 Centre (0,0)
(a)
Triangle A
Triangle with vertices (-1, 5), (-1, 3), (3, 3)
(b)
Triangle B
Triangle with vertices (1, -2), (5, -2), (5, -4)
(c)
Triangle C
Triangle with vertices (1, 1.5), (1, 4), (2, 4)
Correct triangle drawn
Vertices of new triangle at (2, –2) (2, 6) and (6, –2)
12.
(i)
Enlargement scale factor 2 centre (0, 0)
13.
Shape vertices at (3, 1);
14.
15.
Correct triangle drawn Vertices of new triangle at (–1, –4) (–4, 2) and (2, 2)
Vertices at (–2, –1), (–2, –4), (–3, –1)
16
(5, 1), (5, -1), (6, -1)
17.
(a)
3
Vertices at (2, –2), (7, –2), (7, –6), (4, –6), (4, –4), (2, –4) (b) Translation by  
 −1
18.
(a)
(17, 9) (17, 21) (23, 21) Translation (b) (13, 8) (13, 12) (15, 12) Enlargement
(3, 7); (7, 7); (5, 1)
40
Alperton Community School Maths Department: GCSE Grade C Exam Practice