Daily Practice · Higher Plus
March 1978 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1978 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1978
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1978A cuboid measures 7 cm by 7 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd March 1978A bag holds 6 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd March 1978On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 4th March 1978A car covers 870 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.
- 5th March 1978f(x) = 6x - 3 and g(x) = 3x - 6. Work out fg(3).
- 6th March 1978y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 7th March 1978The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 8th March 1978A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 9th March 1978A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 10th March 1978Rationalise the denominator of 54/sqrt(6), giving your answer in its simplest form.
- 11th March 1978The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 12th March 1978y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 9.
- 13th March 1978In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 14th March 1978The probability of winning a game is 1/4. A player expects 11 wins. How many games did they play?
- 15th March 1978On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th March 1978Simplify sqrt(27) + sqrt(108), giving your answer in the form a sqrt(b).
- 17th March 1978A quadratic sequence starts -1, 9, 27, 53. Work out the second difference, and the coefficient of n^2.
- 18th March 1978A train slows steadily from 28 m/s to rest in 8 seconds. Work out its deceleration.
- 19th March 1978In a vector proof you find that vector PQ = a - 4b and vector RS = 3a - 12b. What does this show about PQ and RS?
- 20th March 1978A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 21st March 1978A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 22nd March 1978A rectangle is 18 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd March 1978Solve x^2 + 3x - 10 > 0.
- 24th March 1978y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 25th March 1978A cuboid measures 6 cm by 4 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th March 1978A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th March 1978On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 28th March 1978Expand and simplify (5 + sqrt(10))(5 - sqrt(10)).
- 29th March 1978Write x^2 + 6x + 15 in the form (x + a)^2 + b.
- 30th March 1978y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 31st March 1978A cuboid measures 14 cm by 13 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.