Daily Practice · Higher Plus
October 1988 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1988 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1988
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1988A car covers 190 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.
- 2nd October 1988The point (-2, 0) lies on y = f(x). Write down its image on y = -f(x).
- 3rd October 1988y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 4th October 1988A cuboid measures 4 cm by 8 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th October 1988A bag holds 6 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th October 1988A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 7th October 1988Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 8th October 1988Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 9th October 1988y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 36.
- 10th October 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.
- 11th October 1988A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/22. Work out r.
- 12th October 1988On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 13th October 1988Simplify sqrt(72) + sqrt(98), giving your answer in the form a sqrt(b).
- 14th October 1988f(x) = 5x + 9 and g(x) = 6x - 6. Work out fg(6).
- 15th October 1988A train slows steadily from 37 m/s to rest in 4 seconds. Work out its deceleration.
- 16th October 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.
- 17th October 1988The probability of winning a game is 1/10. A player expects 13 wins. How many games did they play?
- 18th October 1988A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 19th October 1988A rectangle is 11 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th October 1988The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 21st October 1988y is inversely proportional to x^2. When x = 3, y = 36. Work out y when x = 6.
- 22nd October 1988In a vector proof you find that vector PQ = 5a - 3b and vector RS = 15a - 9b. What does this show about PQ and RS?
- 23rd October 1988A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 24th October 1988On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th October 1988Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 26th October 1988A quadratic sequence starts 1, 6, 13, 22. Work out the second difference, and the coefficient of n^2.
- 27th October 1988y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 28th October 1988A cuboid measures 10 cm by 9 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th October 1988A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th October 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?
- 31st October 1988A block has mass 430 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.