Daily Practice · Higher Plus
October 1992 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1992 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1992
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1992In a vector proof you find that vector PQ = a + 5b and vector RS = 5a + 25b. What does this show about PQ and RS?
- 2nd October 1992A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 3rd October 1992On 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?
- 4th October 1992x = 85 and y = 32, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th October 1992Write x^2 + 16x - 12 in the form (x + a)^2 + b.
- 6th October 1992y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 7th October 1992A cuboid measures 15 cm by 6 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th October 1992A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th October 1992A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 10th October 1992A car covers 740 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.
- 11th October 1992Work out the coordinates of the turning point of y = x^2 + 4x - 10.
- 12th October 1992y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 81.
- 13th October 1992A cuboid measures 12 cm by 12 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th October 1992A 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?
- 15th October 1992On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th October 1992Rationalise the denominator of 18/sqrt(2), giving your answer in its simplest form.
- 17th October 1992Simplify (x^2 + 15x + 56)/(x + 7).
- 18th October 1992A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
- 19th October 1992The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 20th October 1992A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 21st October 1992A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?
- 22nd October 1992Simplify sqrt(45) + sqrt(45), giving your answer in the form a sqrt(b).
- 23rd October 1992In an algebraic proof, how would you write an even number in terms of an integer n?
- 24th October 1992y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 25th October 1992In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 26th October 1992The probability of winning a game is 1/10. A player expects 5 wins. How many games did they play?
- 27th October 1992On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th October 1992A rectangle is 27 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th October 1992Make x the subject of 3x + 4 = y(x + 4).
- 30th October 1992y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 31st October 1992In a vector proof you find that vector PQ = 3a - 5b and vector RS = 12a - 20b. What does this show about PQ and RS?