Daily Practice · Higher Plus
March 1977 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1977 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1977
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1977A bag holds 10 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd March 1977A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 3rd March 1977Simplify sqrt(12) + sqrt(75), giving your answer in the form a sqrt(b).
- 4th March 1977In an algebraic proof, how would you write an even number in terms of an integer n?
- 5th March 1977y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 6th March 1977A cuboid measures 10 cm by 12 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th March 1977A bag holds 3 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th March 1977On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 9th March 1977A rectangle is 4 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th March 1977Make x the subject of 8x + 6 = y(x + 6).
- 11th March 1977y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 12th March 1977The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 13th March 1977A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 14th March 1977A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 15th March 1977Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 16th March 1977Write 3/(x + 2) + 7/(x - 3) as a single fraction.
- 17th March 1977y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 9.
- 18th March 1977In 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.
- 19th March 1977The probability of winning a game is 2/5. A player expects 26 wins. How many games did they play?
- 20th March 1977On 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?
- 21st March 1977A block has mass 370 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd March 1977Solve 5x^2 + 19x + 12 = 0.
- 23rd March 1977A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 24th March 1977In a vector proof you find that vector PQ = a + 4b and vector RS = 3a + 12b. What does this show about PQ and RS?
- 25th March 1977A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 26th March 1977A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 27th March 1977x = 36 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th March 1977f(x) = 4x + 10. Work out the inverse function f^-1(x).
- 29th March 1977y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 30th March 1977A cuboid measures 15 cm by 12 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st March 1977A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?