Daily Practice · Higher Plus
March 1992 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1992 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1992
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 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 March 1992A block has mass 380 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.
- 3rd March 1992A quadratic sequence starts 6, 20, 40, 66. Work out the second difference, and the coefficient of n^2.
- 4th March 1992y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 5th March 1992In a vector proof you find that vector PQ = 2a - 5b and vector RS = 6a - 15b. What does this show about PQ and RS?
- 6th March 1992A bag holds 5 red and n blue counters. The probability of taking a red is 5/9. Work out n.
- 7th March 1992A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 8th March 1992x = 45 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th March 1992Solve x^2 + 6x - 7 < 0.
- 10th March 1992y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 81.
- 11th March 1992A cuboid measures 14 cm by 3 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th March 1992A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th March 1992On 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?
- 14th March 1992A car covers 350 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 15th March 1992Write x^2 + 2x - 7 in the form (x + a)^2 + b.
- 16th March 1992A train slows steadily from 24 m/s to rest in 5 seconds. Work out its deceleration.
- 17th March 1992A cuboid measures 7 cm by 14 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th March 1992A bag holds 3 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th March 1992A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 20th March 1992Rationalise the denominator of 24/sqrt(6), giving your answer in its simplest form.
- 21st March 1992Work out the coordinates of the turning point of y = x^2 + 10x - 7.
- 22nd March 1992y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 23rd March 1992The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 24th March 1992A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 25th March 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 March 1992Simplify sqrt(32) + sqrt(72), giving your answer in the form a sqrt(b).
- 27th March 1992Simplify (x^2 + 7x + 6)/(x + 6).
- 28th March 1992y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 29th March 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.
- 30th March 1992The probability of winning a game is 2/5. A player expects 12 wins. How many games did they play?
- 31st March 1992A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?