Daily Practice · Higher Plus
January 1992 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1992 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1992
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1992On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd January 1992Simplify sqrt(20) + sqrt(180), giving your answer in the form a sqrt(b).
- 3rd January 1992Write 6/(x + 2) + 3/(x - 3) as a single fraction.
- 4th January 1992A train slows steadily from 20 m/s to rest in 5 seconds. Work out its deceleration.
- 5th January 1992In a vector proof you find that vector PQ = 5a - 4b and vector RS = 10a - 8b. What does this show about PQ and RS?
- 6th January 1992A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 7th January 1992A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 8th January 1992A rectangle is 12 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th January 1992Solve 15x^2 - 4x - 3 = 0.
- 10th January 1992y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 11th January 1992A cuboid measures 8 cm by 13 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th January 1992A bag holds 5 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th January 1992On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 14th January 1992Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 15th January 1992f(x) = 3x + 7. Work out the inverse function f^-1(x).
- 16th January 1992y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 17th January 1992A cuboid measures 11 cm by 6 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th January 1992A bag holds 6 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th January 1992A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 20th January 1992A block has mass 320 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st January 1992Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 22nd January 1992y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 64.
- 23rd January 1992The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 24th January 1992A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 25th January 1992On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 26th January 1992x = 34 and y = 10, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th January 1992Use the iteration x(n+1) = cube root of (12x(n) + 8) with x(0) = 1. Work out x(1) to 3 decimal places.
- 28th January 1992A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.
- 29th January 1992In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 30th January 1992The probability of winning a game is 1/4. A player expects 13 wins. How many games did they play?
- 31st January 1992A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?