Daily Practice · Higher Plus
June 1988 5-a-day
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The batch download puts all 5 tiers' June 1988 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1988
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1988A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd June 1988On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 3rd June 1988Rationalise the denominator of 49/sqrt(7), giving your answer in its simplest form.
- 4th June 1988Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 5th June 1988y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 6th June 1988A cuboid measures 7 cm by 6 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th June 1988A bag holds 6 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th June 1988A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 9th June 1988Simplify sqrt(27) + sqrt(75), giving your answer in the form a sqrt(b).
- 10th June 1988Use the iteration x(n+1) = cube root of (9x(n) + 8) with x(0) = 5. Work out x(1) to 3 decimal places.
- 11th June 1988y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 9.
- 12th June 1988The 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.
- 13th June 1988A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 14th June 1988On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 15th June 1988A rectangle is 20 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th June 1988Work out the nth term of the quadratic sequence 7, 10, 15, 22, ...
- 17th June 1988A train slows steadily from 33 m/s to rest in 8 seconds. Work out its deceleration.
- 18th June 1988In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 19th June 1988The probability of winning a game is 1/8. A player expects 11 wins. How many games did they play?
- 20th June 1988A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 21st June 1988Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
- 22nd June 1988The point (4, -4) lies on y = f(x). Write down its image on y = -f(x).
- 23rd June 1988y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 24th June 1988In a vector proof you find that vector PQ = 6a + b and vector RS = 24a + 4b. What does this show about PQ and RS?
- 25th June 1988A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 26th June 1988On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 27th June 1988A block has mass 240 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th June 1988Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 29th June 1988y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 30th June 1988A cuboid measures 12 cm by 7 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.