Daily Practice · Higher Plus
August 1988 5-a-day
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The batch download puts all 5 tiers' August 1988 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1988
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1988On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd August 1988Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 3rd August 1988Work out the coordinates of the turning point of y = x^2 + 14x - 13.
- 4th August 1988A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
- 5th August 1988A cuboid measures 14 cm by 6 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th August 1988A bag holds 5 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th August 1988A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 8th August 1988A block has mass 520 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th August 1988Simplify (x^2 + 13x + 42)/(x + 7).
- 10th August 1988y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 11th August 1988The 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.
- 12th August 1988A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 13th August 1988On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 14th August 1988x = 75 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th August 1988In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 9 in terms of an integer n?
- 16th August 1988y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 17th August 1988In 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.
- 18th August 1988The probability of winning a game is 1/2. A player expects 26 wins. How many games did they play?
- 19th August 1988A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 20th August 1988A car covers 140 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.
- 21st August 1988Make x the subject of 8x + 5 = y(x + 5).
- 22nd August 1988y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 16.
- 23rd August 1988In a vector proof you find that vector PQ = 5a - 2b and vector RS = 10a - 4b. What does this show about PQ and RS?
- 24th August 1988A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 25th August 1988On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 26th August 1988Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
- 27th August 1988Write 6/(x + 6) + 2/(x - 1) as a single fraction.
- 28th August 1988A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 29th August 1988A cuboid measures 3 cm by 10 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th August 1988A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st August 1988A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?