NAME__________________________
FORM______
Year 9 Calculator Test 2017
1.
Use your calculator to work out the value of
56 1.42
3.11  54.8
Give your answer correct to 3 significant figures.
………………..
(2)
2.
Ajay sells a pair of shoes for £29 and makes a profit of 16%.
How much did the shoes cost Ajay?
£ ………………..
(3)
3.
(a) The formula for the time T for a satellite to orbit the earth is given by
4 2 R 3
GM
Work out T if R = 6.4 × 106, G = 6.7 × 10–11 and M = 6.0 × 1024.
Give your answer in standard form, correct to 2 significant figures.
T
………………..
(3)
(b) The radius r of a black hole of mass M is given by
2GM
r 2
c
Work out r using the values above and the fact that c = 3 × 108.
Give your answer in standard form, correct to 2 significant figures.
………………..
(3)
4.
A piece of wood is in the shape of a cylinder.
It has a diameter of 2.4 cm and a height of 8.1 cm.
Diagram NOT
accurately drawn
8.1 cm
2.4 cm
Calculate the volume of the wood.
Give your answer correct to 3 significant figures.
Give the units in your answer.
………………..
(4)
5.
Hashim opens a savings account at 5% interest per year.
He puts in £450 and makes no deposits or withdrawals for 3 years.
To the nearest penny, how much money is in the account after 3 years?
£ ………………..
(3)
2
6.
The diagram shows the cross-section of a skate board ramp, which is in the shape of a
semi-circle, inside a rectangle.
Diagram NOT
accurately drawn
8m
(a) Calculate the area of the shaded part of the diagram.
Give your answer correct to 1 decimal place.
……………….. m2
(4)
(b) Calculate the perimeter of the shape.
Give your answer correct to 1 decimal place.
……………….. m
(4)
3
7.
(a) Use the table below to help you draw the graph of y  x2  2 x  4 on the grid.
x
–2
y
4
–1
0
1
–4
–5
1
2
2
3
4
–1
30
25
20
15
10
5
–2
–1
0
0
3
4
5
x
–5
–10
–15
–20
(5)
Question 7 is continued on the next page.
4
(b) Use your graph to find solutions to the equation x2  2x  4  0 .
Give your answers correct to 1 decimal place.
x = ……………….. or ………………..
(2)
8.
P
Diagram NOT
accurately drawn
5.2 m
Q
6.7 m
R
PQR is a right-angled triangle with angle PQR = 90°.
PQ = 5.2 m
QR = 6.7 m
(a)
Calculate the length of PR.
Give your answer correct to 1 decimal place.
……………….. m
(3)
(b)
Calculate the size of angle PRQ.
Give your answer correct to 1 decimal place.
……………….. °
(3)
5
9.
Simplify as powers of 3.
(a) 35  33
………………….……..
(2)
(b) 312  36
………………….……..
(2)
10.
A teacher asked thirty Year 9 students how long they spent brushing their teeth on one
particular day.
She collected their results in a frequency table.
time spent
(t seconds)
number of pupils
0 < t  30
8
30 < t  60
3
60 < t  90
7
90 < t  120
12
Use the blank columns in the table to calculate an estimate for the mean length of time
spent brushing teeth.
Give your answer in minutes and seconds.
……………….. minutes ……………….. seconds
(4)
6
11.
The energy E emitted by a certain object is related to the temperature T as follows:
E T4.
When T is 1000, E is 56 700.
(a) Find an equation for E in terms of T.
E = ………………….……..
(3)
(b) Use your equation to find the energy when the temperature is 100.
………………….…….. W/m2
(2)
12.
Solve these simultaneous equations
2a + 5b = 6
3a – 4b = 32
a = ………………..
b = ………………..
(4)
7
13.
Work out distance h in the diagram below.
Give your answer correct to 1 decimal place.
Diagram NOT
accurately drawn
120°
h
12 cm
h = ………………….…….. cm
(4)
8
14.
Monty is painting a wall. He measures it to the nearest m2 to have an area of 40 m2 (to the
nearest m2). A pot of paint will cover 4m2 (to the nearest m2).
(a) Work out the minimum number of paint pots he may have to use.
……………….. cm
(2)
(b) Work out the maximum number of paint pots he could have to use.
……………….. cm
(2)
15. A chiliagon is a polygon with 1000 sides.
Find the sum of its
(a) interior angles
………………….……..°
(2)
(b) exterior angles
………………….……..°
(2)
***
9
16.
Each of the interior angles in a certain regular polygon is 160°.
Work out how many sides the polygon has.
………………….……..(3)
17.
Make x the subject of these equations.
(a) y  5kx
x = ………….……………..
(2)
(b) l 2  p2  x2
x = ………………….……..
(3)
10
18.
N
N
Diagram NOT
accurately drawn
C
A
220˚
1600 m
B
While orienteering, Billy walks from A to B and then from B to C.
The bearing of B from A is 220˚.
The distance of B from A is 1600 m.
(a) Calculate the bearing of A from B.
………………….…….. ˚
(2)
(b) Calculate the distance AC that Billy travelled to the west.
Give your answer correct to 1 decimal place.
………………….…….. m
(3)
11
19.
Emily writes down three consecutive integers.
She multiplies the third number by 5 and subtracts two lots of the first number.
Then she adds the second number.
Prove that, whatever three consecutive numbers she starts with, her final answer
will always be one less than a multiple of 4.
(4)
TOTAL MARKS FOR THE PAPER = 85
12
NAME__________________________
FORM______
Year 9 Non-Calculator Test 2017
1.
(a) Haresh is buying a T-shirt that usually sells for £9.60.
It is in a sale, all items are reduced by 40%.
Find the new selling price for the T-shirt.
£ ………………..
(2)
(b) In another shop, a poster that cost £7.50 is sold for £12.00.
Calculate the percentage profit.
……………….. %
(2)
2.
Work out 1 54  12  2 13
………………..
(4)
3.
The distance of the dwarf planet Ceres from the sun is about 410 000 000 km.
Write the number 410 000 000 in standard form.
…………….…………..
(2)
4.
(a) The first 5 terms of an arithmetic sequence are
3, 13, 23, 33, 43
Find an expression, in terms of n, for the nth term of the sequence.
………………..
(2)
(b) A quadratic sequence is given by the relation
nth term = 2n2 + 3n
Find the first 3 terms of this sequence.
………………..
(2)
5.
Expand and simplify these expressions.
(a) 5( g  1)  2(3h  g )
……………….………………..
(3)
(b) (e  2)(e 1)
……………….………………..
(3)
2
(c) (g − 4)2
……………….………………..
(3)
6.
Krishan thinks of a number, subtracts 8 and multiplies it by 4. His answer is 8.
(a) Write down an equation for Krishan’s number.
…………………………………….…………..
(2)
(b) Solve the equation to find Krishan’s number.
Krishan’s number is ………………..
(3)
7.
Give the gradients and y-intercepts of the following graphs.
(a)
y = 5x – 1
gradient = ………………..
y-intercept = ………………..
(2)
(b)
2y = x – 1
gradient = ………………..
y-intercept = ………………..
(2)
(c)
y + 2x = 3
gradient = ………………..
y-intercept = ………………..
(2)
3
8.
Factorise fully these expressions.
(a) 6c4  7c2
……………….………………..
(2)
(b) 6 fh 18h
……………….………………..
(2)
(c) 6a2mg  4am2 g 2
……………….………………..
(2)
9.
Factorise fully these quadratic expressions.
(a) 𝑥 2 + 5𝑥 + 6
……………….………………..
(2)
(b) 𝑥 2 − 9
……………….………………..
(2)
10.
Simplify
3 6d
(a)

2d 2 15
………………..
(2)
(b)
4 3

w 2w
………………..
(3)
4
11.
Solve these equations.
(a) 4 f  3  3 f  5
f = ………………..
(3)
(b) 6( j  3)  4 j  32
j = ………………..
(3)
(c)
3
4
(3𝑥 + 1) = 21
x = ………………..
(3)
(d)
2
5
(3r 1)  14 (r  1)  10
r = ………………..
(3)
5
12.
Simplify these ratios:
(a) 35 : 25
………………..
(2)
(b) 4 cm : 1.2 m
………………..
(2)
(c) 2 52 : 3 34
………………..
(3)
***
13.
Using only symbols from the box, make the following into true statements:
Symbols
+ – × ÷ ( )
(a)
2
4
8
= 0
(1)
(b)
2
4
8
= –2
(1)
(c)
2
4
8
= 48
(1)
14.
Solve the inequality
4( x  2)  5x
………………..
(3)
6
15.
The table shows information about the masses of 40 pigs.
mass (m kg)
40  m < 50
50  m < 60
60  m < 70
70  m < 80
80  m < 90
frequency
2
7
12
15
4
(a) Complete the cumulative frequency table.
cumulative
frequency
mass (m kg)
40  m < 50
40  m < 60
40  m < 70
40  m < 80
40  m < 90
(1)
(b) On the grid, draw a cumulative frequency graph for your table.
40
cumulative
frequency
30
20
10
0
40
50
60
70
80
90
mass (m kg)
(2)
(c) Use the graph to find an estimate for the median mass of the pigs.
……………….. kg
(1)
(d) Find an estimate for the interquartile range of the pigs.
……………….. kg
(1)
7
16.
B
A
Diagram NOT
accurately drawn
C
F
E
D
ABCDEF is a regular hexagon.
(a) (i)
Find the size of angle FAB.
……………….. ˚
(1)
(ii) Give a reason for your answer.
……………………………………………………………………………………
……………………………………………………………………………………
(1)
(b) (i)
Find the size of angle ABF.
……………….. ˚
(1)
(ii) Give a reason for your answer.
……………………………………………………………………………………
……………………………………………………………………………………
(1)
(c) Prove that the triangle BDF is equilateral.
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
(2)
TOTAL MARKS FOR THE PAPER = 85
8
Y9 Non-Calculator Test Answers 2017
1.
(a) £5.76
(b) 60%
2. 2
29
30
𝑜𝑟
89
30
3. 4.1 × 108
4. (a) 10n-7
(b) 5,14,27
5. (a) 7g + 5 – 6h
(b) e2 + e – 2
(c) g2 – 8g + 16
6. (a) “Let 𝑥 be the missing number.” (could use a different letter)
4(𝑥 – 8) = 8
(b) 𝑥 = 10 (must be found by solving the equation properly)
7. (a) 5, –1
(b)
1/2, –1/2
(c)
–2, 3
2
2
8. (a) c (6c – 7)
(b) 6h (f – 3)
(c) 2amg (3a + 2mg)
9.(a)
(x+2)(x+3)
(b)
(x+3)(x-3)
3
5d
11
(b)
2w
(𝑎)𝑓
11.
= 8 (𝑏)𝑗 = 7
(𝑐)𝑥 = 9
(𝑑)𝑟 = 7
No marks unless method is clearly ‘doing the same operation to both sides’.
12. (a) 7:5
(b)
1:30 (NO UNITS!) (c)
16:25
13. (a) eg, 2 × 4 – 8 = 0
(b) eg, 2 + 4 – 8 = –2
(c) eg, (2 + 4) × 8 = 48
14. x > -8
10. (a)
15. (a) 2, 9, 21, 36, 40
(b) smooth curve, with cumulative frequencies plotted at the UPPER class
boundaries; eg, the first point plotted after (40, 0) is (50, 2):
(c) anything between 69 and 70 kg
(d) anything between 14 and 16 kg
16. (a) (i)
120°
(ii)
either because it makes a straight line (180°) with 60°, which is the
exterior angle OR because the total interior angle is 4 × 180, and this is shared out
among 6 vertices
(b) (i)
30°
(ii)
Triangle ABF is isosceles, since sides AB and AF are equal (all sides
of a regular polygon are equal), so the base angles AFB and ABF must also be
equal. Since the angles in a triangle add up to 180°, they must both be 30°.
(c) Consider the angles at B, for example. (Exactly the same argument will work
for any other vertex, since the hexagon has 6-fold symmetry.) ABF = 30° (from part
b) and so does CBD, for exactly the same reason. Angle ABC = FAB = 120° (from
part a) so angle FBD = 60°. Similarly the other two angles in the triangle FBD are
60°. So it is equilateral.
Y9 Calculator Test Answers 2017
1. 1.37
2. 29 ÷1.16 = £25
3. (a) 5.1x103
(b) 8.9 × 10–3
i.e., ≈ 9 mm, which is how far the earth would have to be shrunk down in order for
it to become a black hole 
4. 36.6 cm3
5. 450×1.053 = £520.93
6. (a) 8×4 - ½ × π ×42 = 6.9 m2
(b) ½ × π ×8 + 2 × 4 + 8 = 28.6m
7. (a) missing y-values are –1, –4 and 4
(b) –1.2 or 3.2
8. (a) 8.5m
(b) 37.8 °
9. (a) 32
(b) 318
10. total time = 15 × 8 + 45 × 3 + 75 × 7 + 105 × 12 = 2040 sec
2040/30 = 68 sec = 1 min 8 sec
11. (a) E = kT4, sub in 1000 and 56 700 to find k; k = 5.67 × 10–8,
so E = (5.67 × 10–8)T4
(b) 5.67
12. a = 8, b = –2
13. If you draw two right-angled triangles in the ‘roof’ section, then you can use
trigonometry to find that ‘roof height’ = 6 × tan 30 = 3.4641..., so adding on 12
gives h = 15.5 cm
14. (a) 39.5 / 4.5 = 8.777 ie 9 pots
(b) 40.5 / 3.5 = 11.57 ie 12 pots
15. (a) 998×180 = 179640°
(b) 360°
16. 180 – 160 = 20; 360/20 = 18 sides
17. (a) x = y/(5k)
(b) x =  l 2  p 2 condone no ±
18. (a) 220 - 180 = 40°
(b) 1600 × sin 40 = 1028.5 m
19. “Let the three numbers be x-1, x and x+1.” (oe)
5(x+1) – 2(x-1) + x = 5x + 5 – 2x + 2 + x = 4x + 7.
4x + 8 would have to be a multiple of 4, and 4x + 7 is one less.
TDA