WJEC GCSE Mathematics Unit 1: Non-calculator Higher June 2017 question paper 3300U50-1

Ceri has a set of cards.

Each of her cards is labelled North, East, South or West.

The table below shows the probability distribution when a card is taken from the set of cards at

Ceri chooses one card at random from her set of cards.

What is the probability that the card is labelled East or South?

Sasha has an identical set of cards. Ceri and Sasha each choose one card at random from their set of cards.

What is the probability that they both choose a card labelled North?

The table below shows some of the values of y = x² – 5x + 2, for values of x from –1 to 5.

Complete the table above.

On the graph paper below, draw the graph of y = x² – 5x + 2 for values of x from

Draw the line y = –3 on the graph paper.

Write down the values of x where the line y = –3 cuts the curve y = x² – 5x + 2.

Give your answers correct to 1 decimal place.

Express 700 as a product of its prime factors in index form.

(b)

Explain how this tells you that 33 554 432 is not a square number.

Which one of the following equations could represent the line shown in the graph above?

Circle your answer.

y = – x – 2 y = – x + 2 y = x + 2 y = x – 2 y = – x.

Which one of the following points lies on the line 2y = 3x + 4?

Circle your answer.

(2, –5) (5, 2) (–2, 5) (2, 5) (–2, –5)

What is the gradient of the line shown in the graph above?

Circle your answer.

A group of 20 people visited Anglesey for a weekend break.

• 10 of the group visited Beaumaris Castle. • 13 of the group visited South Stack Lighthouse. • 4 of the group did not visit either of these places.

Complete the Venn diagram below to show this information.

The universal set, , contains all of the 20 people in the group.

One person is chosen at random from the group.

What is the probability that this person visited only one of the two places?

A, B and C are points on the circumference of a circle.

XY is a tangent to the circle at the point A.

BAY = 74° and ABC = 53°. Prove that triangle ABC is an isosceles triangle. You must give a reason for any statement that you make or any calculation that you carry out.

On the graph paper below, draw the region which satisfies all of the following inequalities.

What is the greatest possible value of x such that all three conditions are met?

What is the greatest possible value of y such that all three conditions are met?

SSS, SAS, ASA and RHS are notations used to describe the conditions required to prove that two triangles are congruent. [S ≡ Side, A ≡ Angle, R ≡ Right angle and H ≡ Hypotenuse.]

The following triangles are not drawn to scale. For each pair of triangles, circle the correct statement.

Using the axes below, sketch the graph of y = sin x for values of x from 0° to 360°.

You must label any important values on both axes.

The diagram shows two rectangles.

The combined area of both rectangles is 50 cm². By considering the areas of the two rectangles, show that 2x² – 5x – 25 = 0 and hence find the

value of x.

A bag contains 6 red blocks, 4 green blocks and 2 yellow blocks.

Three blocks are taken from the bag, at random, without replacement.

What is the probability that the first block removed is red, the second is green and the

third is yellow?

Calculate the probability that all three blocks will be the same colour.

Write down the probability that the three blocks will not be the same colour.

The graph of y = x² has been drawn below, for values of x from x = 0 to x = 6.

Use the trapezium rule, with the ordinates x = 0, x = 1, x = 2, x = 3, x = 4, x = 5 and x = 6, to

estimate the area of the shaded region shown above.

By considering algebraic expressions, show that it will never be possible for the surface area of

a sphere of radius r to be equal to the surface area of a cube with sides of length r.