4MA1 Mathematics A: January 2019 Paper 1HHigher Tier Paper 1

(a)Factorise fully 4p + 6pq[2]

(b)Expand and simplify (e + 3)(e – 5)[2]

(c)Solve y = 2 y + 15

Show clear algebraic working.

[3]

(a)Describe fully the single transformation that maps triangle A onto triangle B.[3]

(b)On the grid, translate triangle A by the vector  2

Label the new triangle C.[1]

The table gives information about the price of gold.

(a)Work out the percentage increase in the price of gold between 1st February 2016 and 1st March 2016 Give your answer correct to 3 significant figures.

[3]

The price of one ounce of gold on 1st February 2016 was 1126.50 dollars. The price of gold increased by 19% from 1st February 2016 to 1st July 2016

(b)Work out the price of one ounce of gold on 1st July 2016 Give your answer correct to the nearest dollar.

[3]

BCD and AFE are straight lines.

Show that BCD is parallel to AFE. Give reasons for your working.[5]

(a)Complete the table of values for y = x²– 5x + 6

[1]

(b)On the grid, draw the graph of y = x²– 5x + 6 for 0  x  5

[2]

(c)By drawing a suitable straight line on the grid, find estimates for the solutions of the equation

[3]

The table shows the volumes, in km³, of four oceans.

Atlantic Ocean ´⁸

Southern Ocean ´⁷

(a)Write 7.18 ´ 10⁷ as an ordinary number.[1]

(b)Calculate the total volume of these four oceans.

[2]

The volume of the South China Sea is 9 880 000 km³

(c)Write 9 880 000 in standard form.[1]

The diagram shows an isosceles triangle.

The area of the triangle is 12 cm²

Work out the perimeter of the triangle. Give your answer correct to 3 significant figures.

[4]

The table shows information about the speeds of 60 cycles.

10 < s  20

20 < s  30

30 < s  40

40 < s  50

50 < s  60

(a)Complete the cumulative frequency table.

[1]

(b)On the grid, draw a cumulative frequency graph for your table.

[2]

(c)Use your graph to find an estimate for the interquartile range of the speeds.

[2]

Here is triangle ABD.

The point C lies on BD.

Calculate the size of angle BAC. Give your answer correct to 1 decimal place.

[5]

Express − as a single fraction in its simplest terms.

[3]

The curve C has equation y = 13 x³ − 9x + 1

(a)Find

[2]

(b)Find the range of values of x for which C has a negative gradient.[3]

All the students in Year 11 at a school must study at least one of Geography (G), History (H) and Religious Studies (R).

In Year 11 there are 65 students.

Of these students

15 study Geography, History and Religious Studies 21 study Geography and History 16 study Geography and Religious Studies 30 study Geography 18 study only Religious Studies 37 study Religious Studies

(a)Using this information, complete the Venn diagram to show the number of students in each region of the Venn diagram.

[3]

A student in Year 11 who studies both History and Religious Studies is chosen at random.

(b)Work out the probability that this student does not study Geography.[2]

T is directly proportional to the cube of r

T = 21.76 when r = 4

(a)Find a formula for T in terms of r[3]

(b)Work out the value of T when r = 6[1]

The total surface area of a solid hemisphere is equal to the curved surface area of a cylinder.

The radius of the hemisphere is r cm. The radius of the cylinder is twice the radius of the hemisphere.

Given that

find the value of m.

[4]

(a)Rationalise the denominator of a +a − 4b4b where a is an integer and b is a prime number.

Simplify your answer.

[3]

(b)Given that  yx  = xy_m where x ≠ y

find the value of m.

[1]

Here is triangle ABC.

Calculate the value of x. Give your answer correct to 3 significant figures.[5]

The graph of y = f(x) is shown on the grid.

(a)On the grid above, sketch the graph of y = f  1 2 x  [2]

The graph of y = f(x + k) is shown on the grid below.

(b)Write down the value of k[1]

g is the function with domain x  –3 such that g(x) = x²+ 6x

(a)Write down the range of g^–1[1]

(b)Express the inverse function g^–1 in the form g^–1 : x 

[4]

A bowl contains n pieces of fruit. Of these, 4 are oranges and the rest are apples.

Two pieces of fruit are going to be taken at random from the bowl.

The probability that the bowl will then contain (n – 6) apples is 13

Work out the value of n Show your working clearly.[6]

(2x + 23), (8x + 2) and (20x – 52) are three consecutive terms of an arithmetic sequence.

Prove that the common difference of the sequence is 12[4]