Top-Notch
Guide
To
Mathematics
Designed to improve the number of students achieving grade C at GCSE
M.Woodfine
Shape, Space And Measure
Shape, Space And Measure
Shape, Space And Measure
Question Time – Shape, Space And Measure
1.
The diagram shows a shape.
Work out the area of the shape.
…………………………… cm2
(Total 4 marks)
2.The diameter of a circle is 12 centimetres.
(a)Work out the circumference of the circle.
Give your answer, in centimetres, correct to 1 d.p.
...... cm
(2)
The length of each diagonal of a square is 20 cm.
(b)Work out the area of the square.
...... cm2
(2)
(Total4marks)
3.
(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 , centre O.
Label your new triangle C. (3)
(Total 5 marks)
Algebra
Algebra
Question Time – Algebra
1.(a)Simplify
(i)3g + 5g......
(ii)2r × 5p...... (2)
(b)Expand5(2y – 3)...... (1)
(c)Expand and simplify2(3x + 4) – 3(4x – 5) ...... (2)
(Total 5 marks)
2.(a)Factorise3t – 12 ...... (1)
(b)Expand and simplify3(2x – 1) – 2(2x – 3)...... (2)
(Total 3 marks)
3.A straight line has equation y = 4x – 5.
(a)Find the value of x when y = 1.x = ...... (2)
(b)Rearrange the equation y = 4x – 5 to find x in terms of y.
x = ...... (2)
(Total 4 marks)
4.(a)Work out the value of 3p + 4q when p = 5 and q = –2
...... (2)
(b)Given that y = 4x – 3, work out the value of x when y = 11
x = ...... (3)
(Total 5 marks)
5.On the grid, draw the graph of y = 2x – 3
Use values of x from x = –1 to x = 4 (Total 3 marks)
6.The first term of a sequence is 7. The rule for the sequence is Add 5 to the previous term.
(a)Write down the second term and the third term of the sequence.
....……… , …………… (1)
(b)Work out the 10th term of the sequence...... (2)
(c)Write down an expression, in terms of n, for the nth term of the sequence.
...... (2)
(Total 5 marks)
7.Solve the simultaneous equations
2x + 3y = 6
3x − 2y = 22
x = ……………………y = ……………………
(Total 4 marks)
Number
Number
Number
Question Time – Number
1.(a) Estimate the value of...... (2)
(Total 2 marks)
2.(a)Write the number 56 392 correct to one significant figure...... (1)
(b)Write the number 0.0436 correct to one significant figure...... (1)
(Total 2 marks)
3.The cost of 4 kg of apples is £3.36. The total cost of 3 kg of apples and 2.5 kg of pears is £4.12Work out the cost of 1 kg of pears. Give your answer in pence...... p
(Total3marks)
4.(a)Work out ………………………(2)
(b)Work out 5 – 2………………………(3)
(Total 5 marks)
5.Write these numbers in order of size.
Start with the smallest number.
(i)......
(ii)5, – 6, – 10, 2, – 4......
(iii), , , ......
(Total 5 marks)
6.A customer who cancels a holiday with Funtours has to pay a cancellation charge.
The cancellation charge depends on the number of days before the departure date the customer cancels the holiday. The cancellation charge is a percentage of the cost of the holiday. The table shows the percentages.
The cost of Amy’s holiday was £840.
She cancelled her holiday 25 days before the departure date.
(a)Work out the cancellation charge she had to pay. £……… (2)
The cost of Carol’s holiday was £600.
She cancelled her holiday and had to pay a cancellation charge of £480.
(b)Work out £480 as a percentage of £600.…………………………. %(2)
Ravi cancelled his holiday 30 days before the departure date. He had to pay a cancellation charge of £272.
(c)Work out the cost of his holiday.£ ……………………………(2)
(Total 6 marks)
Handling Data
Handling Data
Question Time – Handling Data
1.Anil counted the number of letters in each of 30 sentences in a newspaper.
Anil showed his results in a stem and leaf diagram.
0 / 8 / 8 / 91 / 1 / 2 / 3 / 4 / 4 / 8 / 9
2 / 0 / 3 / 5 / 5 / 7 / 7 / 8
3 / 2 / 2 / 3 / 3 / 6 / 6 / 8 / 8
4 / 1 / 2 / 3 / 3 / 5
2.The table shows information about the number of hours that 120 children used a computer last week.
Work out an estimate for the mean number of hours that the children used a computer.
Give your answer correct to 2 decimal places.
……………… hours
(Total 4 marks)
3.Rosie had 10 boxes of drawing pins. She counted the number of drawing pins in each box.
The table gives information about her results.
Work out the mean number of drawing pins in a box.
......
(Total 3 marks)
4.A bag contains 6 red disks, 4 blue disks and 5 green disks.
A fair dice has 4 faces painted red and the other 2 faces painted blue.
Lisa takes a disk at random from the bag and records its colour.
Lisa then throws the dice twice and each time records the colour of the face it lands on.
Work out the probability that, of the three colours Lisa records, exactly two are the same.
………………………
(Total 5 marks)
5.Mr Smith is going to sell drinks on his coaches.
He wants to know what type of drinks people like. He designs a questionnaire.
Design a suitable questionnaire, which he could use to find out what type of drink people like.
(Total 2 marks)