Daily Practice · Higher Plus
March 1959 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1959 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1959
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1959A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 2nd March 1959A block has mass 470 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 3rd March 1959Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 4th March 1959y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 5th March 1959A cuboid measures 3 cm by 3 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th March 1959A bag holds 7 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th March 1959On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 8th March 1959x = 147 and y = 10, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th March 1959f(x) = 5x - 6 and g(x) = 6x + 9. Work out fg(3).
- 10th March 1959y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 11th March 1959A cuboid measures 5 cm by 7 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th March 1959A bag holds 6 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th March 1959A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 14th March 1959A 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.
- 15th March 1959The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 16th March 1959y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 16.
- 17th March 1959The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 18th March 1959A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 19th March 1959On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 20th March 1959Rationalise the denominator of 35/sqrt(5), giving your answer in its simplest form.
- 21st March 1959A quadratic sequence starts 9, 20, 37, 60. Work out the second difference, and the coefficient of n^2.
- 22nd March 1959A train slows steadily from 39 m/s to rest in 5 seconds. Work out its deceleration.
- 23rd March 1959In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 24th March 1959The probability of winning a game is 1/10. A player expects 9 wins. How many games did they play?
- 25th March 1959A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 26th March 1959Simplify sqrt(12) + sqrt(27), giving your answer in the form a sqrt(b).
- 27th March 1959Solve x^2 - 10x + 16 > 0.
- 28th March 1959y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
- 29th March 1959In a vector proof you find that vector PQ = 5a - 6b and vector RS = 15a - 18b. What does this show about PQ and RS?
- 30th March 1959A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 31st March 1959On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?