Daily Practice · Higher Plus
June 1991 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' June 1991 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1991In an algebraic proof, how would you write an even number in terms of an integer n?
- 2nd June 1991A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd June 1991In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 4th June 1991The probability of winning a game is 7/8. A player expects 105 wins. How many games did they play?
- 5th June 1991A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 6th June 1991Simplify sqrt(20) + sqrt(20), giving your answer in the form a sqrt(b).
- 7th June 1991Make x the subject of 7x + 7 = y(x + 7).
- 8th June 1991y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 9th June 1991In a vector proof you find that vector PQ = 2a + 4b and vector RS = 4a + 8b. What does this show about PQ and RS?
- 10th June 1991A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 11th June 1991On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 12th June 1991A rectangle is 4 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th June 1991Write 6/(x - 4) + 4/(x + 4) as a single fraction.
- 14th June 1991y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 15th June 1991A cuboid measures 5 cm by 6 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th June 1991A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th June 1991A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 18th June 1991Expand and simplify (8 + sqrt(7))(8 - sqrt(7)).
- 19th June 1991Solve 8x^2 + 6x + 1 = 0.
- 20th June 1991y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 81.
- 21st June 1991A cuboid measures 12 cm by 7 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd June 1991A bag holds 3 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd June 1991On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th June 1991A block has mass 720 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th June 1991f(x) = 4x + 8. Work out the inverse function f^-1(x).
- 26th June 1991A train slows steadily from 22 m/s to rest in 10 seconds. Work out its deceleration.
- 27th June 1991The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 28th June 1991A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 29th June 1991A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 30th June 1991x = 93 and y = 57, each correct to the nearest whole number. Work out the upper bound of x - y.