Questions and Worked Solutions for Edexcel GCSE 9 - 1 Mathematics Specimen Paper 1 Higher (No Calculator).

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Edexcel GCSE 9 - 1 Mathematics Specimen Past Paper 1 Higher (Pdf)

Edexcel GCSE 9 - 1 Specimen Paper 1 Higher (No Calculator) Solutions

For questions 1 - 7, refer to questions 20 - 26 of the Foundation Paper

Edexcel GCSE 9 - 1 Specimen Paper 1 (No Calculator) Solutions for Questions 8 - 23

1. The diagram shows a right-angled triangle.

Work out the size of the smallest angle of the triangle.

2. A box exerts a force of 140 newtons on a table.

The pressure on the table is 35 newtons/m

Calculate the area of the box that is in contact with the table.

3. There are only red counters, blue counters, green counters and yellow counters in a bag.

The table shows the probabilities of picking at random a red counter and picking at random a yellow counter.

Colour: red, blue, green, yellow

Probability: 0.24, 0.32

The probability of picking a blue counter is the same as the probability of picking a green counter.

Complete the table.

4. A pattern is made using identical rectangular tiles.

Find the total area of the pattern.

5. The diagram shows a sand pit.

The sand pit is in the shape of a cuboid.

Sally wants to fill the sand pit with sand.

A bag of sand costs £2.50

There are 8 litres of sand in each bag.

Sally says,

“The sand will cost less than £70”

Show that Sally is wrong.

6. Four friends each throw a biased coin a number of times.

The table shows the number of heads and the number of tails each friend got.

The coin is to be thrown one more time.

(a) Which of the four friends' results will give the best estimate for the probability that the coin will land heads?

Justify your answer.

Paul says,

“With this coin you are twice as likely to get heads as to get tails.”

(b) Is Paul correct?

Justify your answer.

The coin is to be thrown twice.

(c) Use all the results in the table to work out an estimate for the probability that the coin will land heads both times.

7. (a) Write down the exact value of cos30°

(b) Given that sin30° = 0.5, work out the value of x.

8. The mass of Jupiter is 1.899 × 1027 kg.

The mass of Saturn is 0.3 times the mass of Jupiter.

(a) Work out an estimate for the mass of Saturn.

Give your answer in standard form.

(b) Give evidence to show whether your answer to (a) is an underestimate or an overestimate.

9. Walkden Reds is a basketball team.

At the end of 11 games, their mean score was 33 points per game.

At the end of 10 games, their mean score was 2 points higher.

Jordan says,

“Walkden Reds must have scored 13 points in their 11th game.”

Is Jordan right?

You must show how you get your answer.

10. There are some red counters and some yellow counters in a bag.

There are 30 yellow counters in the bag.

The ratio of the number of red counters to the number of yellow counters is 1:6

(a) Work out the number of red counters in the bag.

Riza puts some more red counters into the bag.

The ratio of the number of red counters to the number of yellow counters is now 1:2

(b) How many red counters does Riza put into the bag?

12. Sean drives from Manchester to Gretna Green.

He drives at an average speed of 50 mph for the first 3 hours of his journey.

He then has 150 miles to drive to get to Gretna Green.

Sean drives these 150 miles at an average speed of 30 mph.

Sean says,

“My average speed from Manchester to Gretna Green was 40 mph.”

Is Sean right?

You must show how you get your answer.

13. m = √(k

Make k the subject of the formula.

14. Solve (x + 2)/3x + (x - 2)/2x = 3

15. Show that (2x

can be written in the form (ax + b)/(cx + d)

where a, b, c and d are integers.

16. These graphs show four different proportionality relationships between y and x.

Match each graph with a statement in the table below.

Proportionality relationship Graph letter

y is directly proportional to x

y is inversely proportional to x

y is proportional to the square of x

y is inversely proportional to the square of x

17. PQ = PR.

S is the midpoint of PQ.

T is the midpoint of PR.

Prove triangle QTR is congruent to triangle RSQ.

18. The diagram shows a solid hemisphere.

Volume of sphere = 4/3 πr

Surface area of sphere = 4πr

The volume of the hemisphere is 250/3 π

Work out the exact total surface area of the solid hemisphere.

Give your answer as a multiple of π.

19. Simplify fully (6 - √5)(6 + √5)/√31

You must show your working.

20. Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.

21. There are 10 pens in a box.

There are x red pens in the box.

All the other pens are blue.

Jack takes at random two pens from the box.

Find an expression, in terms of x, for the probability that Jack takes one pen of each colour.

Give your answer in its simplest form.

22. CAYB is a quadrilateral.

CA = 3a

CB = 6b

BY = 5a – b

X is the point on AB such that AX : XB = 1 : 2

Prove that CX = 2/5 CY

23. Find an equation of the line that passes through C and is perpendicular to AB.

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