Daily Practice · Higher Plus
March 1995 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1995 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1995
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1995A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
- 2nd March 1995A cuboid measures 9 cm by 9 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd March 1995A bag holds 4 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th March 1995A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 5th March 1995x = 86 and y = 19, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th March 1995The point (1, 5) lies on y = f(x). Write down its image on y = f(-x).
- 7th March 1995y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 8th March 1995The 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.
- 9th March 1995A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 10th March 1995On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 11th March 1995A car covers 710 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th March 1995Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 13th March 1995y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 14th March 1995In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 15th March 1995The probability of winning a game is 2/5. A player expects 6 wins. How many games did they play?
- 16th March 1995A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 17th March 1995Rationalise the denominator of 15/sqrt(3), giving your answer in its simplest form.
- 18th March 1995f(x) = 6x - 8 and g(x) = 5x + 4. Work out fg(3).
- 19th March 1995y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 49.
- 20th March 1995In a vector proof you find that vector PQ = 2a - 3b and vector RS = 8a - 12b. What does this show about PQ and RS?
- 21st March 1995A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 22nd March 1995On 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?
- 23rd March 1995Simplify sqrt(45) + sqrt(45), giving your answer in the form a sqrt(b).
- 24th March 1995The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 25th March 1995A train slows steadily from 28 m/s to rest in 10 seconds. Work out its deceleration.
- 26th March 1995A cuboid measures 11 cm by 5 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th March 1995A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th March 1995A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 29th March 1995A rectangle is 17 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th March 1995A quadratic sequence starts 9, 21, 41, 69. Work out the second difference, and the coefficient of n^2.
- 31st March 1995y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.