Daily Practice · Higher Plus
May 1989 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1989 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1989
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1989y is inversely proportional to x^2. When x = 5, y = 72. Work out y when x = 6.
- 2nd May 1989A cuboid measures 6 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd May 1989A bag holds 6 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th May 1989On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 5th May 1989Rationalise the denominator of 35/sqrt(5), giving your answer in its simplest form.
- 6th May 1989f(x) = 4x - 4 and g(x) = 2x - 8. Work out fg(-1).
- 7th May 1989y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 8th May 1989The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 9th May 1989A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 10th May 1989A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 11th May 1989Simplify sqrt(75) + sqrt(108), giving your answer in the form a sqrt(b).
- 12th May 1989The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 13th May 1989y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 64.
- 14th May 1989In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 15th May 1989The probability of winning a game is 7/8. A player expects 63 wins. How many games did they play?
- 16th May 1989On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th May 1989A rectangle is 26 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th May 1989A quadratic sequence starts 11, 25, 47, 77. Work out the second difference, and the coefficient of n^2.
- 19th May 1989A train slows steadily from 21 m/s to rest in 4 seconds. Work out its deceleration.
- 20th May 1989In a vector proof you find that vector PQ = a + 5b and vector RS = 2a + 10b. What does this show about PQ and RS?
- 21st May 1989A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 22nd May 1989A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 23rd May 1989Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 24th May 1989Solve x^2 - 8x + 7 < 0.
- 25th May 1989y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 26th May 1989A cuboid measures 13 cm by 6 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th May 1989A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th May 1989On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 29th May 1989A block has mass 530 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th May 1989Write x^2 + 4x + 10 in the form (x + a)^2 + b.
- 31st May 1989y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.