Daily Practice · Higher Plus
June 1989 5-a-day
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The batch download puts all 5 tiers' June 1989 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1989
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1989A cuboid measures 7 cm by 5 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd June 1989A bag holds 5 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd June 1989A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 4th June 1989x = 55 and y = 7, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th June 1989Work out the coordinates of the turning point of y = x^2 - 4x - 4.
- 6th June 1989y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 4.
- 7th June 1989The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 8th June 1989A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 9th June 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?
- 10th June 1989A car covers 370 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 11th June 1989Simplify (x^2 + 8x + 15)/(x + 5).
- 12th June 1989A train slows steadily from 20 m/s to rest in 5 seconds. Work out its deceleration.
- 13th June 1989In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 14th June 1989The probability of winning a game is 5/8. A player expects 25 wins. How many games did they play?
- 15th June 1989A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 16th June 1989Rationalise the denominator of 70/sqrt(7), giving your answer in its simplest form.
- 17th June 1989In an algebraic proof, how would you write an odd number in terms of an integer n?
- 18th June 1989y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 19th June 1989In a vector proof you find that vector PQ = 2a - 4b and vector RS = 4a - 8b. What does this show about PQ and RS?
- 20th June 1989A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 21st June 1989On 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?
- 22nd June 1989Simplify sqrt(20) + sqrt(80), giving your answer in the form a sqrt(b).
- 23rd June 1989Make x the subject of 6x + 3 = y(x + 3).
- 24th June 1989y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 25th June 1989A cuboid measures 3 cm by 8 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th June 1989A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th June 1989A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 28th June 1989A rectangle is 29 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th June 1989Write 3/(x - 2) + 7/(x + 1) as a single fraction.
- 30th June 1989y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 4.