Grade C/D Revision for Higher Calculator Paper
Recipe Questions
1.
Here are the ingredients needed to make 16 gingerbread men.
Ingredients
to make 16 gingerbread men
180 g
40 g
110 g
30 g
flour
ginger
butter
sugar
Hamish wants to make 24 gingerbread men.
Work out how much of each of the ingredients he needs.
..........................................................g flour
.......................................................g ginger
........................................................g butter
.........................................................g sugar
(Total for Question 1 is 3 marks)
Product of Prime Factors
13.
(a) Express 180 as a product of its prime factors.
..........................................
(Total for Q13 3 marks)
Expanding Brackets
11.
(a) Expand
4(3x + 5)
......................................................................
(1)
(b) Expand and simplify
2(x – 4) + 3(x + 5)
......................................................................
(2)
(c) Expand and simplify
(x + 4)(x + 6)
......................................................................
(2)
(Total for Question 11 is 5 marks)
Translation
5.
Describe the single transformation that maps triangle A onto triangle B
Enlargement
(b) On the grid, enlarge triangle B by scale factor 3, centre (0, 0).
(2)
(Total for Question 9 is 2 marks)
Probability
8.
There are only red counters, blue counters, white counters and black counters in a bag.
The table shows the probability that a counter taken at random from the bag will be red or blue.
Colour
red
blue
Probability
0.2
0.5
white
black
The number of white counters in the bag is the same as the number of black counters in the
bag.
Tania takes at random a counter from the bag.
(a) Work out the probability that Tania takes a white counter.
...................................................
(2)
There are 240 counters in the bag.
(b) Work out the number of red counters in the bag.
...................................................
(2)
(Total for Question 8 is 4 marks)
Trial and Improvement
11.
The equation
x3 – 6x = 72
has a solution between 4 and 5
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show all your working.
x = ..............................................
(Total for Question 11 is 4 marks)
Estimated Mean
14.
The table gives information about the temperature, T °C, at noon in a town for 50 days.
Temperature (T °C)
Frequency
8 < T ≤ 12
6
12 < T ≤ 16
8
16 < T ≤ 20
13
20 < T ≤ 24
21
24 < T ≤ 28
2
(a) Write down the modal class interval.
..........................................
(1)
(b) Calculate an estimate for the mean temperature
........................................... °C (4)
Exchange Rates
*10. In the UK, petrol costs £1.24 per litre.
In the USA, petrol costs 3.15 dollars per US gallon.
1 US gallon = 3.79 litres
£1 = 1.47 dollars
Is petrol cheaper in the UK or in the USA?
Total (4 marks)
Area and Circumference of Circles
4.
Here is a circle.
The diameter of the circle is 9 cm.
Work out the circumference of this circle.
Give your answer correct to 3 significant figures.
.......................................... cm
(Total for Question 4 is 2 marks)
*5. Mr Weaver’s garden is in the shape of a rectangle.
In the garden there is a patio in the shape of a rectangle and two ponds in the shape of circles
with diameter 3.8 m.
The rest of the garden is grass.
Mr Weaver is going to spread fertiliser over all the grass.
One box of fertiliser will cover 25 m2 of grass.
How many boxes of fertiliser does Mr Weaver need?
You must show your working.
(Total for Question 5 is 5 marks)
Straight Line Graphs
4.
On the grid, draw the graph of y = 3x – 2 for values of x from –1 to 3
(Total for Question 4 is 3 marks)
Nth term
5.
Here are the first 5 terms of an arithmetic sequence.
3
9
15
21
27
(a) Find an expression, in terms of n, for the nth term of this sequence.
............................................
(2
Ben says that 150 is in the sequence.
(b) Is Ben right?
You must explain your answer.
(1)
(Total for Question 5 is 3 marks)
Algebra and Shape
11.
The diagram shows a parallelogram.
The sizes of the angles, in degrees, are
2x
3x – 15
2x
2x + 24
Work out the value of x.
x = ..............................................
(Total for Question 27 is 3 marks)
Using a Calculator
2.
(a) Use your calculator to work out
38.5  14.2
.
18.4  5.9
Write down all the figures on your calculator display.
You must give your answer as a decimal.
..............................................
(2)
(b) Write your answer to part (a) correct to 1 significant figure.
..............................................
(1)
(Total for Question 2 is 3 marks)
Inequalities
10.
m is an integer such that –2 < m  3
(a) Write down all the possible values of m.
.............................................................................................
(2)
(b) Solve 7x – 9 < 3x + 4
..............................................(2)
(Total for Question 10 is 4 marks)