1
Here are five numbers: 0.7, 3/5, 0.68, 5/8, 71%.
Non-calculator
ORIGINAL
Write these five numbers in order of size. Start with the smallest number.
(2)
(Total for Question 1 is 2 marks)
Pearson Edexcel GCSE (9–1) Mathematics
Number — topic question pack
1MA1
Original practice paper written in the style of Edexcel papers — not a Pearson publication. This pack is untiered and can include both Foundation and Higher content.
Name: __________________________________
Class: __________________________________
Answer every question. Show all stages of your working. The total number of marks is 56.
This topic pack mixes calculator and non-calculator practice. Each question states whether a calculator may be used.
Question paper
2
In a box, 2/5 of the counters are red and the rest are blue. There are 18 red counters.
Non-calculator
ORIGINAL
Work out the number of blue counters in the box.
(2)
(Total for Question 2 is 2 marks)
3
Work out an estimate for (38.2 × 5.9) ÷ 0.21.
Non-calculator
ORIGINAL
(a)Show that a suitable estimate is 1200.
(2)
(b)Is your estimate larger or smaller than the exact answer? Give a reason.
(1)
(Total for Question 3 is 3 marks)
4
Work out, giving each answer as a mixed number in its simplest form.
Non-calculator
ORIGINAL
(a)2 1/3 + 1 3/4
(2)
(b)4 2/5 − 1 7/10
(2)
(Total for Question 4 is 4 marks)
5
Work out the following, taking care with negative numbers and order of operations.
Non-calculator
ORIGINAL
(a)−5 − (−8) + (−3)
(1)
(b)(−4)² − 3 × (−2)
(2)
(Total for Question 5 is 3 marks)
6
Work out the following.
Either calculator policy
ORIGINAL
(a)3/4 of 60
(1)
(b)35% of 220
(1)
(Total for Question 6 is 2 marks)
7
This question is about prime factors, HCF and LCM.
Non-calculator
ORIGINAL
(a)Write 84 as a product of its prime factors.
(2)
(b)Given that 120 = 2³ × 3 × 5, find the highest common factor (HCF) of 84 and 120.
(1)
(c)Find the lowest common multiple (LCM) of 84 and 120.
(1)
(Total for Question 7 is 4 marks)
8
This question is about surds. Give each answer in its simplest form.
Non-calculator
ORIGINAL
(a)Simplify √50.
(2)
(b)Rationalise the denominator of 6/√3.
(2)
(Total for Question 8 is 4 marks)
9
Write 0.45 as a fraction in its simplest form.
Non-calculator
ORIGINAL
Give your answer as a fraction in its simplest form.
(1)
(Total for Question 9 is 1 mark)
10
Work out the following, using a formal written method. You must show your working.
Non-calculator
ORIGINAL
(a)Work out 347 × 26
(2)
(b)Work out 546 ÷ 14
(2)
(Total for Question 10 is 4 marks)
11
This question is about rounding and accuracy.
Non-calculator
ORIGINAL
(a)Round 6.7482 to 2 decimal places.
(1)
(b)Round 3849 to 2 significant figures.
(1)
(c)A length L is 24 cm, measured to the nearest centimetre. Use inequalities to write down the error interval for L.
(2)
(Total for Question 11 is 4 marks)
12
Write down the value of each of the following.
Non-calculator
ORIGINAL
(a)5³
(1)
(b)√81
(1)
(c)the cube root of 27
(1)
(Total for Question 12 is 3 marks)
13
A café offers a set meal. There are 4 different starters, 6 different main courses and 3 different desserts. A meal is one starter, one main course and one dessert.
Non-calculator
ORIGINAL
(a)Work out the number of different meals that can be made.
(2)
(b)A password is made from 2 letters (each from A to Z, letters may repeat) followed by 1 digit (0 to 9). Work out the number of different possible passwords.
(2)
(Total for Question 13 is 4 marks)
14
This question is about money and time.
Calculator
ORIGINAL
(a)A worker is paid £11.50 per hour. She works 7.5 hours on each of 5 days. Work out her total pay for the 5 days.
(2)
(b)A train leaves a station at 09:48. The journey takes 2 hours 35 minutes. Work out the time the train arrives.
(2)
(Total for Question 14 is 4 marks)
15
This question is about standard form.
Either calculator policy
ORIGINAL
(a)Write 4 700 000 in standard form.
(1)
(b)Write 3.2 × 10⁻⁴ as an ordinary number.
(1)
(c)Work out (3 × 10⁵) × (2 × 10³). Give your answer in standard form.
(2)
(Total for Question 15 is 4 marks)
16
Two lighthouses can be seen from a harbour. One lighthouse flashes every 12 seconds. The other lighthouse flashes every 18 seconds. At 8 pm exactly, both lighthouses flash at the same time.
Non-calculator
ORIGINAL
(a)Work out the number of seconds after 8 pm when the two lighthouses next flash at the same time.
(2)
(b)A third lighthouse flashes every 8 seconds and also flashes at 8 pm exactly. Work out the number of seconds after 8 pm when all three lighthouses next flash at the same time.
(2)
(Total for Question 16 is 4 marks)
17
Work out the following, using the correct priority of operations.
Non-calculator
ORIGINAL
(a)5 + 3 × 4
(1)
(b)(8 − 2)² ÷ 4
(2)
(c)20 − 6 ÷ 2
(1)
(Total for Question 17 is 4 marks)
Pearson Edexcel GCSE (9–1) Mathematics
Mark scheme — Number
1
Answer: 3/5, 5/8, 0.68, 0.7, 71%
M1 for converting all five numbers to a common form (e.g. decimals: 0.7, 0.6, 0.68, 0.625, 0.71). A1 for the fully correct order 3/5, 5/8, 0.68, 0.7, 71% (accept the decimal/percentage equivalents in the same order).
2 marks
2
Answer: 27
M1 for a complete method, e.g. 18 ÷ 2 × 5 = 45 (total) then 45 − 18, or 3/5 of the total using 18 = 2/5. A1 for 27.
2 marks
3
(a)
Answer: 40 × 6 ÷ 0.2 = 240 ÷ 0.2 = 1200
M1 for rounding each number to 1 significant figure (40, 6 and 0.2). A1 for a correct evaluation leading to 1200.
(b)
Answer: Larger (an overestimate), because 38.2 and 5.9 were rounded up while 0.21 was rounded down, and dividing by a smaller number makes the result larger.
B1 for larger / overestimate with a valid reason (numerator rounded up and/or dividing by a smaller number).
3 marks
4
(a)
Answer: 4 1/12
M1 for a correct common denominator, e.g. 28/12 + 21/12 (or 7/3 + 7/4). A1 for 49/12 or 4 1/12.
(b)
Answer: 2 7/10
M1 for a correct common denominator, e.g. 44/10 − 17/10. A1 for 27/10 or 2 7/10.
4 marks
5
(a)
Answer: 0
B1 for 0.
(b)
Answer: 22
M1 for correctly evaluating 16 and −6 (i.e. squaring and multiplying before subtracting). A1 for 22.
3 marks
6
(a)
Answer: 45
B1 for 45.
(b)
Answer: 77
B1 for 77.
2 marks
7
(a)
Answer: 2² × 3 × 7
M1 for a correct method (factor tree or repeated division) reaching primes. A1 for 2² × 3 × 7 (accept 2 × 2 × 3 × 7).
(b)
Answer: 12
B1 for 12 (product of the common primes 2² × 3; ft their factorisation of 84).
(c)
Answer: 840
B1 for 840 (2³ × 3 × 5 × 7; ft their factorisation).
4 marks
8
(a)
Answer: 5√2
M1 for √25 × √2 (or √(25 × 2)). A1 for 5√2.
(b)
Answer: 2√3
M1 for multiplying numerator and denominator by √3, giving 6√3/3. A1 for 2√3.
4 marks
9
Answer: 9/20
B1 for 9/20 (from 45/100 simplified).
1 mark
10
(a)
Answer: 9022
M1 for a complete correct method (e.g. long multiplication or a grid with all partial products) with not more than one arithmetic error. A1 for 9022.
(b)
Answer: 39
M1 for a complete correct division method (e.g. short/long division or building up multiples of 14). A1 for 39.
4 marks
11
(a)
Answer: 6.75
B1 for 6.75.
(b)
Answer: 3800
B1 for 3800.
(c)
Answer: 23.5 ≤ L < 24.5
B1 for 23.5 as the lower bound and 24.5 as the upper bound. B1 for the fully correct interval 23.5 ≤ L < 24.5 (accept ≤ … < convention).
4 marks
12
(a)
Answer: 125
B1 for 125.
(b)
Answer: 9
B1 for 9.
(c)
Answer: 3
B1 for 3.
3 marks
13
(a)
Answer: 72
M1 for 4 × 6 × 3. A1 for 72.
(b)
Answer: 6760
M1 for 26 × 26 × 10. A1 for 6760.
4 marks
14
(a)
Answer: £431.25
M1 for 11.50 × 7.5 × 5 (or 11.50 × 37.5). A1 for 431.25.
(b)
Answer: 12:23
M1 for a correct time method (e.g. 09:48 + 2 h = 11:48, then + 35 min). A1 for 12:23.
4 marks
15
(a)
Answer: 4.7 × 10⁶
B1 for 4.7 × 10⁶.
(b)
Answer: 0.00032
B1 for 0.00032.
(c)
Answer: 6 × 10⁸
M1 for 3 × 2 = 6 and 10⁵ × 10³ = 10⁸ (or 600 000 000). A1 for 6 × 10⁸.
4 marks
16
(a)
Answer: 36 seconds
M1 for a correct method to find the LCM of 12 and 18 (e.g. listing multiples, or 2² × 3²). A1 for 36.
(b)
Answer: 72 seconds
M1 for a correct method to find the LCM of 12, 18 and 8 (e.g. 2³ × 3²). A1 for 72.
4 marks
17
(a)
Answer: 17
B1 for 17 (multiplication before addition).
(b)
Answer: 9
M1 for 6² = 36 (brackets then power). A1 for 9.
(c)
Answer: 17
B1 for 17 (division before subtraction).
4 marks