Daily Practice · Higher Plus
November 1977 5-a-day
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The batch download puts all 5 tiers' November 1977 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1977
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1977A cuboid measures 7 cm by 13 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd November 1977A bag holds 6 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd November 1977On 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?
- 4th November 1977Rationalise the denominator of 21/sqrt(7), giving your answer in its simplest form.
- 5th November 1977Work out the nth term of the quadratic sequence 3, 20, 45, 78, ...
- 6th November 1977y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 7th November 1977The 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.
- 8th November 1977A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 9th November 1977A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 10th November 1977Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
- 11th November 1977The point (0, -2) lies on y = f(x). Write down its image on y = f(x - 1).
- 12th November 1977y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 49.
- 13th November 1977In 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 November 1977The probability of winning a game is 5/8. A player expects 50 wins. How many games did they play?
- 15th November 1977On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th November 1977A rectangle is 12 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th November 1977Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 18th November 1977A train slows steadily from 20 m/s to rest in 5 seconds. Work out its deceleration.
- 19th November 1977In a vector proof you find that vector PQ = 3a - b and vector RS = 9a - 3b. What does this show about PQ and RS?
- 20th November 1977A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 21st November 1977A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 22nd November 1977Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).
- 23rd November 1977f(x) = 4x - 9 and g(x) = 5x + 1. Work out fg(6).
- 24th November 1977y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 25th November 1977A cuboid measures 3 cm by 7 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th November 1977A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th November 1977On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th November 1977A block has mass 670 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th November 1977The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 30th November 1977y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.