Daily Practice · Higher Plus
September 1988 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1988 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1988
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1988Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 2nd September 1988Solve 8x^2 + 18x - 5 = 0.
- 3rd September 1988y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 4th September 1988A cuboid measures 6 cm by 6 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th September 1988A bag holds 5 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th September 1988On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th September 1988A rectangle is 27 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th September 1988f(x) = 7x + 7. Work out the inverse function f^-1(x).
- 9th September 1988y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 10th September 1988The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 11th September 1988A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
- 12th September 1988A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 13th September 1988Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
- 14th September 1988Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 15th September 1988y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 16.
- 16th September 1988In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 17th September 1988The probability of winning a game is 3/10. A player expects 15 wins. How many games did they play?
- 18th September 1988On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 19th September 1988A block has mass 670 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th September 1988Use the iteration x(n+1) = cube root of (7x(n) + 3) with x(0) = 4. Work out x(1) to 3 decimal places.
- 21st September 1988A train slows steadily from 25 m/s to rest in 10 seconds. Work out its deceleration.
- 22nd September 1988In a vector proof you find that vector PQ = 6a + 6b and vector RS = 12a + 12b. What does this show about PQ and RS?
- 23rd September 1988A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 24th September 1988A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 25th September 1988x = 127 and y = 10, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th September 1988Work out the nth term of the quadratic sequence 3, 14, 33, 60, ...
- 27th September 1988y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 28th September 1988A cuboid measures 11 cm by 9 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th September 1988A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th September 1988On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?