Pearson Edexcel GCSE (9–1) Mathematics
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 65.
This topic pack mixes calculator and non-calculator practice. Each question states whether a calculator may be used.
1
This question tests standard geometric vocabulary.
Non-calculator
(a)Two straight lines meet at right angles. What word describes these lines?
(1)
(b)What is the mathematical name for a polygon with four sides?
(1)
(c)How many vertices does a pentagon have?
(1)
(Total for Question 1 is 3 marks)
2
A garden sprinkler is fixed at a point P in the middle of a large flat lawn. The sprinkler waters every part of the lawn that is within 4 m of P.
Non-calculator
(a)Describe fully the boundary of the watered region.
(1)
(b)A long straight path crosses the lawn. Describe the locus of all points that are exactly 2 m from the path.
(1)
(Total for Question 2 is 2 marks)
3
This question is about the properties of quadrilaterals.
Non-calculator
(a)Write down one property that a rhombus always has but a general parallelogram does not.
(1)
(b)A quadrilateral has exactly one pair of parallel sides. Write down its mathematical name.
(1)
(c)Explain why every square is also a rectangle.
(1)
(Total for Question 3 is 3 marks)
4
In triangle ABC, AB = 7 cm, BC = 5 cm and angle ABC = 40°. In triangle PQR, PQ = 7 cm, QR = 5 cm and angle PQR = 40°.
Non-calculator
(a)Using the correct abbreviation, state the criterion that shows triangle ABC is congruent to triangle PQR.
(1)
(b)Hence write down the length of PR compared with the length of AC.
(1)
(Total for Question 4 is 2 marks)
5
Triangle T has vertices A(1, 1), B(1, 4) and C(3, 1). Triangle T is enlarged by scale factor 2, with centre the origin (0, 0), to give triangle T′.
Non-calculator
(a)Write down the coordinates of the images of A, B and C after the enlargement.
(2)
(b)The area of triangle T is 3 cm². Write down the area of triangle T′.
(2)
(Total for Question 5 is 4 marks)
6
A shape is reflected in the x-axis and then the image is reflected in the y-axis.
Non-calculator
(a)Describe fully the single transformation that maps the original shape onto the final image.
(2)
(b)A point on the original shape has coordinates (a, b). Write down its coordinates on the final image.
(1)
(Total for Question 6 is 3 marks)
7
This question is about the properties of 3D solids.
Non-calculator
(a)How many faces does a triangular prism have?
(1)
(b)How many edges does a square-based pyramid have?
(1)
(c)How many vertices does a cuboid have?
(1)
(Total for Question 7 is 3 marks)
8
This question is about converting between standard units.
Non-calculator
(a)Change 2.5 litres into millilitres.
(1)
(b)Change 3.4 kg into grams.
(1)
(c)A film lasts 135 minutes. Write this time in hours and minutes.
(1)
(Total for Question 8 is 3 marks)
9
The point A(3, −2) is translated to the point B(−1, 5).
Non-calculator
(a)Write down the column vector that describes the translation from A to B.
(1)
(b)The same translation maps the point C(0, 4) onto the point D. Work out the coordinates of D.
(2)
(Total for Question 9 is 3 marks)
10
A trapezium has parallel sides of length 8 cm and 12 cm, and a perpendicular height of 5 cm.
Calculator
(a)Work out the area of the trapezium.
(2)
(b)A prism has this trapezium as its cross-section and a length of 9 cm. Work out the volume of the prism.
(2)
(Total for Question 10 is 4 marks)
11
The sizes of the three angles of a triangle, in degrees, are x + 20, 2x and 3x − 20.
Non-calculator
(a)Form an equation in x and solve it to find the value of x.
(3)
(b)Write down the size of the largest angle.
(1)
(c)Is the triangle acute-angled, right-angled or obtuse-angled? Give a reason.
(1)
(Total for Question 11 is 5 marks)
12
A right-angled triangle has its two shorter sides of length 6 cm and 8 cm, with the right angle between them.
Calculator
(a)Work out the length of the hypotenuse.
(2)
(b)Work out the area of the triangle.
(1)
(c)In a different right-angled triangle the side opposite angle θ is 5 cm and the hypotenuse is 13 cm. Work out the size of angle θ, giving your answer to 1 decimal place.
(2)
(Total for Question 12 is 5 marks)
13
A circle has radius 7 cm. Use the π button on your calculator.
Calculator
(a)Work out the area of the circle, giving your answer to 3 significant figures.
(2)
(b)Work out the circumference of the circle, giving your answer to 3 significant figures.
(2)
(Total for Question 13 is 4 marks)
14
A sector of a circle has radius 9 cm and a sector angle of 80°. Use the π button on your calculator.
Calculator
(a)Work out the arc length of the sector, giving your answer to 3 significant figures.
(2)
(b)Work out the area of the sector, giving your answer to 3 significant figures.
(2)
(Total for Question 14 is 4 marks)
15
This question is about the areas of 2D shapes.
Non-calculator
(a)A parallelogram has base 9 cm and perpendicular height 6 cm. Work out its area.
(2)
(b)A triangle has base 10 cm and perpendicular height 7 cm. Work out its area.
(1)
(Total for Question 15 is 3 marks)
16
This question is about angle facts.
Non-calculator
(a)Three angles lie on a straight line. Their sizes are x°, 2x° and 90°. Work out the value of x.
(2)
(b)Two of the angles in a triangle are 55° and 80°. Work out the size of the third angle, and give a reason for your answer.
(2)
(Total for Question 16 is 4 marks)
17
A ship sails from a port P.
Non-calculator
(a)The ship sails from P to a point Q on a bearing of 070°. Work out the bearing of P from Q (the back bearing).
(2)
(b)A lighthouse L is due east of P. Write down the bearing of L from P.
(1)
(Total for Question 17 is 3 marks)
18
This question uses Pythagoras' theorem. Give your answers in the units stated.
Calculator
(a)A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. Work out the length of the other shorter side.
(2)
(b)A straight ladder of length 5 m leans against a vertical wall. The foot of the ladder is 1.4 m from the base of the wall. Work out how far up the wall the ladder reaches. Give your answer in metres.
(2)
(Total for Question 18 is 4 marks)
19
Triangle ABC is isosceles with AB = AC. The angle at the apex, angle BAC, is 40°.
Non-calculator
(a)Work out the size of angle ABC. Give a reason for your answer.
(2)
(b)A different isosceles triangle has each of its two equal base angles equal to 50°. Work out the size of the apex angle.
(1)
(Total for Question 19 is 3 marks)
Pearson Edexcel GCSE (9–1) Mathematics
1
(a)
Answer: Perpendicular
B1 for perpendicular.
(b)
Answer: Quadrilateral
B1 for quadrilateral.
(c)
Answer: 5
B1 for 5.
3 marks
2
(a)
Answer: A circle of radius 4 m with its centre at P (the watered region is everywhere on or inside this circle).
B1 for a circle of radius 4 m centred on P (accept the region inside such a circle).
(b)
Answer: Two straight lines parallel to the path, one on each side, each 2 m from the path.
B1 for two lines parallel to the path, 2 m either side of it.
2 marks
3
(a)
Answer: All four sides are equal in length (accept: the diagonals cross at right angles).
B1 for a correct distinguishing property (all sides equal, or diagonals perpendicular).
(b)
Answer: Trapezium
B1 for trapezium.
(c)
Answer: A square has four right angles and two pairs of parallel, equal opposite sides, which is exactly the definition of a rectangle, so a square satisfies it.
B1 for a correct reason referring to four right angles (and opposite sides parallel/equal) meeting the definition of a rectangle.
3 marks
4
(a)
Answer: SAS
B1 for SAS.
(b)
Answer: PR = AC (they are equal).
B1 for PR equal to AC.
2 marks
5
(a)
Answer: A′(2, 2), B′(2, 8), C′(6, 2)
M1 for multiplying the coordinates by 2 (at least one image correct). A1 for all three: (2, 2), (2, 8), (6, 2).
(b)
Answer: 12 cm²
M1 for using an area scale factor of 2² (= 4). A1 for 12 (cm²).
4 marks
6
(a)
Answer: A rotation of 180° about the origin (0, 0).
B2 for rotation 180° about the origin (B1 for rotation 180°, or B1 for a rotation about the origin).
(b)
Answer: (−a, −b)
B1 for (−a, −b).
3 marks
7
(a)
Answer: 5
B1 for 5.
(b)
Answer: 8
B1 for 8.
(c)
Answer: 8
B1 for 8.
3 marks
8
(a)
Answer: 2500 ml
B1 for 2500 (ml).
(b)
Answer: 3400 g
B1 for 3400 (g).
(c)
Answer: 2 hours 15 minutes
B1 for 2 hours 15 minutes.
3 marks
9
(a)
Answer: The column vector with top number −4 and bottom number 7, i.e. (−4, 7) written as a column.
B1 for the column vector with top −4 and bottom 7.
(b)
Answer: (−4, 11)
M1 for applying the translation to C, e.g. (0 + (−4), 4 + 7). A1 for (−4, 11).
3 marks
10
(a)
Answer: 50 cm²
M1 for ½ × (8 + 12) × 5. A1 for 50.
(b)
Answer: 450 cm³
M1 for 50 × 9 (cross-sectional area × length; ft their area from (a)). A1 for 450.
4 marks
11
(a)
Answer: x = 30
M1 for (x + 20) + 2x + (3x − 20) = 180. M1 for 6x = 180. A1 for x = 30.
(b)
Answer: 70°
B1 for 70 (from 3x − 20 with x = 30; the three angles are 50°, 60°, 70°).
(c)
Answer: Acute-angled, because its largest angle is 70°, which is less than 90° (so all three angles are less than 90°).
B1 for acute-angled with a reason referring to the largest angle (70°) being less than 90° (ft their angles).
5 marks
12
(a)
Answer: 10 cm
M1 for 6² + 8² (= 36 + 64 = 100). A1 for 10.
(b)
Answer: 24 cm²
B1 for 24 (from ½ × 6 × 8).
(c)
Answer: 22.6°
M1 for sin θ = 5/13. A1 for 22.6 (accept 22.6°; 22.61… rounded).
5 marks
13
(a)
Answer: 154 cm²
M1 for π × 7² (= π × 49). A1 for 154 (accept 153.9 to 154).
(b)
Answer: 44.0 cm
M1 for 2 × π × 7 (or π × 14). A1 for 44.0 (accept 43.98 to 44.0).
4 marks
14
(a)
Answer: 12.6 cm
M1 for 80/360 × 2 × π × 9 (or 80/360 × π × 18). A1 for 12.6 (accept 12.56 to 12.6).
(b)
Answer: 56.5 cm²
M1 for 80/360 × π × 9². A1 for 56.5 (accept 56.5 to 56.55).
4 marks
15
(a)
Answer: 54 cm²
M1 for 9 × 6. A1 for 54.
(b)
Answer: 35 cm²
B1 for 35 (from ½ × 10 × 7).
3 marks
16
(a)
Answer: x = 30
M1 for x + 2x + 90 = 180 (angles on a straight line sum to 180). A1 for x = 30.
(b)
Answer: 45° because the angles in a triangle add up to 180°.
B1 for 45. B1 for the reason: angles in a triangle sum to 180°.
4 marks
17
(a)
Answer: 250°
M1 for 070 + 180. A1 for 250°.
(b)
Answer: 090°
B1 for 090° (accept 90°).
3 marks
18
(a)
Answer: 12 cm
M1 for 13² − 5² (= 169 − 25 = 144). A1 for 12.
(b)
Answer: 4.8 m
M1 for 5² − 1.4² (= 25 − 1.96 = 23.04). A1 for 4.8.
4 marks
19
(a)
Answer: 70° because the base angles of an isosceles triangle are equal and the three angles add up to 180°, so each base angle is (180 − 40) ÷ 2 = 70°.
M1 for (180 − 40) ÷ 2. A1 for 70° with a reason referring to equal base angles / angle sum 180°.
(b)
Answer: 80°
B1 for 80 (180 − 2 × 50).
3 marks