Daily Practice · Higher Plus
July 1988 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1988 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1988
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1988A bag holds 6 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd July 1988A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 3rd July 1988x = 57 and y = 19, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th July 1988f(x) = 6x - 1 and g(x) = 4x + 9. Work out fg(4).
- 5th July 1988y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 81.
- 6th July 1988A cuboid measures 9 cm by 5 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th July 1988A bag holds 3 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th July 1988On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th July 1988A car covers 740 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th July 1988The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 11th July 1988A train slows steadily from 36 m/s to rest in 5 seconds. Work out its deceleration.
- 12th July 1988The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 13th July 1988A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 14th July 1988A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 15th July 1988Rationalise the denominator of 15/sqrt(5), giving your answer in its simplest form.
- 16th July 1988A quadratic sequence starts 4, 15, 30, 49. Work out the second difference, and the coefficient of n^2.
- 17th July 1988y is inversely proportional to x^2. When x = 3, y = 75. Work out y when x = 5.
- 18th July 1988In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 19th July 1988The probability of winning a game is 3/4. A player expects 24 wins. How many games did they play?
- 20th July 1988On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 21st July 1988Simplify sqrt(27) + sqrt(108), giving your answer in the form a sqrt(b).
- 22nd July 1988Solve x^2 + 9x + 8 < 0.
- 23rd July 1988y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 24th July 1988In a vector proof you find that vector PQ = 2a + 4b and vector RS = 10a + 20b. What does this show about PQ and RS?
- 25th July 1988A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 26th July 1988A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 27th July 1988A rectangle is 21 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th July 1988Write x^2 - 10x + 13 in the form (x + a)^2 + b.
- 29th July 1988y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 36.
- 30th July 1988A cuboid measures 11 cm by 11 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st July 1988A 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?